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All Textbook Solutions for Calculus and Its Applications (11th Edition)

These review exercises are for test preparation. They can also serve as a practice test. Answers are at the back of the book Red bracketed section references indicate the part(s) of the chapter to restudy if your answer is incorrect Concept Reinforcement For each equation in column A, select the most appropriate graph in column B. [R.1, R.4, R.5] Column A Column B y=|x|These review exercises are for test preparation. They can also serve as a practice test. Answers are at the back of the book Red bracketed section references indicate the part(s) of the chapter to restudy if your answer is incorrect Concept Reinforcement For each equation in column A, select the most appropriate graph in column B. [R.1, R.4, R.5] 2. Column A Column B These review exercises are for test preparation. They can also serve as a practice test. Answers are at the back of the book Red bracketed section references indicate the part(s) of the chapter to restudy if your answer is incorrect Concept Reinforcement For each equation in column A, select the most appropriate graph in column B. [R.1, R.4, R.5] 3. Column A Column B These review exercises are for test preparation. They can also serve as a practice test. Answers are at the back of the book Red bracketed section references indicate the part(s) of the chapter to restudy if your answer is incorrect Concept Reinforcement For each equation in column A, select the most appropriate graph in column B. [R.1, R.4, R.5] 4. Column A Column B These review exercises are for test preparation. They can also serve as a practice test. Answers are at the back of the book Red bracketed section references indicate the part(s) of the chapter to restudy if your answer is incorrect Concept Reinforcement For each equation in column A, select the most appropriate graph in column B. [R.1, R.4, R.5] Column A Column B g(x)=x These review exercises are for test preparation. They can also serve as a practice test. Answers are at the back of the book Red bracketed section references indicate the part(s) of the chapter to restudy if your answer is incorrect Concept Reinforcement For each equation in column A, select the most appropriate graph in column B. [R.1, R.4, R.5] 6. Column A Column B These review exercises are for test preparation. They can also serve as a practice test. Answers are at the back of the book Red bracketed section references indicate the part(s) of the chapter to restudy if your answer is incorrect Concept Reinforcement For each equation in column A, select the most appropriate graph in column B. [R.1, R.4, R.5] Column A Column B f(x)=1x In Exercises 8 14, classify each statement as either true or false. The graph of an equation represents all ordered pairs that are solutions of the equation. [R.1]In Exercises 8 14, classify each statement as either true or false. If f(3)=5 and f(3)=5, then f cannot be a function. [R.2]In Exercises 8 14, classify each statement as either true or false. The notation (3,7) can represent a point or an interval. [R.3]In Exercises 8 14, classify each statement as either true or false. An equation of the form yy1=m(xx1) has a graph that is a line of slope m passing through (x1,y1).In Exercises 8 14, classify each statement as either true or false. The graph of an equation of the form f(x)=ax2+bx+c has its vertex at x=b/(2a). [R.5]In Exercises 8 – 14, classify each statement as either true or false. 13. A scatterplot is a random collection of points near a line. In Exercises 8 – 14, classify each statement as either true or false. 14. Unless stated otherwise the domain of a polynomial function is the set of all real numbers. 15. Hearing-impaired Americans. The following graph shows the number of hearing-impaired Americans who are x years old. (Source: Better Hearing Institute.) a. What is the number of hearing-impaired Americans aged 40? b. For what age(s) are about 3,000,000 Americans hearing impaired? c. What is a reasonable estimate of the domain of this function? Why? Finance: compound interest. Sam borrows $4000 at 12%, compounded annually. How much does she owe at the end of 2 yr? [R.1]17. Business: compound interest. Suppose $1100 is invested at 5%, compounded semiannually. How much is in the account at the end of 4 yr? Is the following correspondence a function? Why or why not? [R.2] Not a function. One input, Elizabeth, has three outputs.A function is given by f(x)=x2+x. Find each of the following. [R.2] a. f(3) b. f(5) c. f(a) d. f(x+h)Graph. [R.5] f(x)=(x2)2 Graph. 21. Graph. 22. Graph. [R.5] g(x)=x+1 Use the vertical-line test to determine whether each of the following is the graph of a function. 24. Use the vertical-line test to determine whether each of the following is the graph of a function. [R.2]Use the vertical-line test to determine whether each of the following is the graph of a function. [R.2]Use the vertical-line test to determine whether each of the following is the graph of a function. 27. For the graph of function f shown to the right determine (a) f(2), (b) the domain, (c) all x-values for which f(x)=2; and (d) the range. [R.3]29. Consider the function given by a. Find and. b. Graph the function. 30. Write interval notation for each graph. a. b. c. Write interval notation for each of the following. Then graph each interval on a number line. a. {x4x5} b. {xx2}For the function graphed below, determine (a) f(3); (b) the domain; (c) all x-values for which f(x)=4; (d) the range. [R.3]33. Find the domain of f. a. b. 34. What are the slope and the y-intercept of? 35. Find an equation of the line with slope, containing the point. Find the slope of the line containing the points (2,5) and (3,10). [R.4]Find the average rate of change. 37. Find the average rate of change. [R.4]Business: shipping charges. The amount A that Pet-Treats-to-U charges for shipping is directly proportional to the value V of the item(s) being shipped. If the business charges $2.10 to ship a $60 gift basket, find an equation of variation expressing A as a function of V. [R.4]40. Business: profit-and-loss analysis. The band Soul Purpose has fixed costs of $4000 for producing a new CD. Thereafter, the variable costs are $0.50 per CD, and the CD will sell for $10. [R.4] a. Find and graph the total cost of producing x CDs. b. Find and graph the total revenue from the sale of x CDs. Use the same axes as in part (a) c. Find and graph the total profit from the production and sale of x CDs. Use the same axes as in part (b). d. How many CDs must the band sell m order to break even? 41RE Graph each of the following. If the graph is a parabola, identify the vertex. [R.5] a. f(x)=x26x+8 b. g(x)=x3+2 c. y=1x d. y=x2+x6x2 Solve each of the following. [R.5] a. 5+x2=4x+2 b. 2x2=4x+3 44RE 45. Rewrite each of the following as an equivalent expression using radical notation. a. b. c. d. Determine the domain of the function given by f(x)=2x98. [R.5]Graph each of the following, and identify the y-intercept. [R.5] a. y=12(4)x b. y=3(14)x 48. Economics: equilibrium point. Find the equilibrium point for the given demand and supply functions. Demand: Supply: (assume ) Trail maintenance. The amount of time required to maintain a section of the Appalachian Trail vanes inversely with the number of volunteers working. If a particular section of trail can be cleared in 4 hr by 9 volunteers how long would it take 11 volunteers to clear the same section? [R.5]50. Life science: maximum heart rate. A person exercising should not exceed a maximum heart rate, which depends on his or her gender, age, and resting heart rate. The following table shows data relating resting heart rate and maximum heart rate for a 20-yr-ald woman. Resting Heart Rate, r (in beats per minute) Maximum Heart Rate, M (in beats per minute) 50 170 60 172 70 174 80 176 (Source: American Heart Association) a. Using the data points (50, 170) and (80, 176), find a linear function that fits the data. b. Graph the scatterplot and the function on the same set of axes. c. Use the function to predict the maximum heart rate of a woman whose resting heart rate is 67. Business: ticket profits. The Spring Valley Drama Troupe is performing a new play Data relating daily profit P to the number of days after opening night appear below. [R.6] Days, x 0 9 18 27 36 45 Profit, P (in dollars) 870 548 100 100 510 872 a. Make a scatterplot of the data. b. Do the data seem to fit a quadratic function? Data fit a quadratic function. c. Using the data points (0, 870), (18, -100), and (45, 872), find a quadratic function that fits the data. d. Use the function from part (c) to estimate the profit made on the 30th day. e. Make an estimate of the domain of this function. Why must it have restrictions?52. Economics: demand. The demand function for Clifton Cheddar Cheese is given by Demand: where x is the price per pound and q is in thousands of pounds. a. Find the number of pounds sold when the price per pound is $6.50. b. Find the price per pound when 720,000 lb are sold. 53RE 54RE 55. Approximate the point(s) of intersection of the graphs of the two functions in Exercises 53 and 54. Life science: maximum heart rate. Use the data in Exercise 50. [R.6] a. Use regression to fit a linear function to the data. b. Use the linear function to predict the maximum heart rate of a woman whose resting heart rate is 67. c. Compare your answer to that found in Exercise 50. Are the answers equally reliable? Why or why not?57RE Social Sciences: time spent on home computer. The data in the table below relate A, the average number of minutes spent per month on a home computer, to a person's age, x, in years. [R.6] a. Use regression to fit linear quadratic, cubic and quartic functions to the data. b. Make a scatterplot of the data, and graph each function on the scatterplot. c. Which function provides the best model for the data? Why? Age (in years) Average Use (in minutes per month) 6.5 363 14.5 645 21 1377 29.5 1727 39.5 1696 49.5 2052 55 2299 (Source: Media Matrix; The PC Meter Company)Business: compound interest. Cecilia invests funds at 6.5% compounded annually. The investment grows to $798.75 in 1 yr. How much was originally invested?Two-year college tuitions. Find the average rate of change of the tuition and fees at public two-year colleges. (Source: U.S. National Center for Education Statistics, Digest of Education Statistics, annual)Find the slope and they-intercept of the graph of y=45x23.4. Find an equation of the line with slope, containing the point. Find the slope of the line containing the points (9,2) and (3,4).Find the average rate of change.Find the average rate of change. 7. Life Science: body fluids. The weight F of fluids in a human is directly proportional to body weight W. It is known that a 180-lb person has 120 lb of fluids. Find an equation of variation expressing F as a function of W.9. Business: profit-and-loss analysis. A printing shop has fixed costs of $8000 for producing a newly designed note card. The variable costs are $0.08 per card. The revenue from each card will be $0.50. a. Find, the total cost of producing x cards. b. Find, the total revenue from the sale of x cards. c. Find, the total profit from the production and sale of x cards. d. How many cards must the company sell in order to break even? Economics: equilibrium point. Find the equilibrium point for these demand and supply functions. Demand: q=(x8)2,0x8 Supply: q=x2+x+13 given that x is the unit price, in dollars, and q is the quantity demanded or supplied, in thousands.Use the vertical-line test to determine whether each of the following is the graph of a function.Use the vertical-line test to determine whether each of the following is the graph of a function.13. For the following graph of a quadratic function f, determine (a); (b) the domain, (c) all x-values for which and (d) the range. Graph: f(x)=8/x.15T 16T Graph: f(x)=x21x+1 Determine the domain of each function. f(x)=x2+20x2+5x14 Determine the domain of each function. f(x)=x3x+6 20. Write interval notation for the following graph. Graph: f(x)={x2+2,forx0,x22,forx0.Graph and identify the y-intercept: f(x)=12(3)x.Nutrition. As people age their daily caloric needs change. The following table shows data for physically active females, relating age, in years, to number of calories needed daily. Age Number of Calories Needed Daily 6 1800 11 2200 16 2400 24 2400 41 2200 (Source: Based on data from US Department of Agriculture) a. Make a scatterplot of the data. b. Do the data appear to fit a quadratic function? c. Using the data points (6, 1800), (16, 2400), and (41, 2200), find a quadratic function that fits the data. d. Use the function from part (c) to predict the number of calories needed daily by a physically active 30 yr-old woman. e. What restrictions are reasonable for the domain of the function from part (c)? Why?24. Simplify: . 25. Find the domain and the zeros of the function given by . Write an equation that has exactly three solutions: 3, 1, and 4.27. A function's average rate of change over the interval is. If, find. Graph f and find its zeros, domain, and range: f(x)=|9x2|31.29. Nutrition. Use the data in Exercise 23. a. Use regression to fit a quadratic function to the data. b. Use the function from part (a) to predict the number of calories needed daily by a physically active 30-yr-old woman. c. c) Compare your answer from part (b) with that from part (d) of Exercise 23. Which answer do you feel is more accurate? Why? 1. a. Using REGRESSION, find a linear function that fits the data. b. Graph the linear function. c. Use the linear function to predict the average price of a movie ticket in 2015 and in 2020. Do these estimates appear reasonable? d. Use the function to predict the year when the average price of a ticket will reach $20. Does this estimate seem reasonable? 2. a. Using REGRESSION, find a quadratic function, that fits the data. b. Graph the quadratic function. c. Use the quadratic function to predict the average price of a movie ticket in 2015 and in 2020. Do these estimates appear reasonable? d. Use the function to predict the year when the average price of a ticket will reach $20. Does this estimate seem reasonable? 3. a. Using REGRESSION, find a cubic function, that fits the data. b. Graph the cubic function. c. Use the cubic function to predict the average price of a movie ticket in 2015 and in 2020. Do these estimates appear reasonable? d. Use the function to predict the year when the average price of a ticket will reach $20. Does this estimate seem reasonable? a. Using regression, find a quartic function, y=ax4+bx3+cx2+dx+e, that fits the data. y=0.000002x40.00023x3+0.0098x20.067x+0.558 b. Graph the quartic function. c. Use the quartic function to predict the average price of a movie ticket in 2015 and in 2020. Do these estimates appear reasonable? d. Use the function to predict the year when the average price of a ticket will reach $20. Does this estimate seem reasonable?a. Using regression, find an exponential function, y=a0ax, hat fits the data. y=0.521453(1.049459)x b. Graph the exponential function. c. Use the exponential function to predict the average price of a movie ticket in 2015 and 2020. Do these estimates appear reasonable? d. Use the function to predict the year when the average price of a ticket will reach $20. Does this estimate seem reasonable?You are a research statistician assigned the task of making an accurate prediction of movie ticket prices. a. Why might you not use the linear function? b. Why might you use the quadratic function rather than the linear function? c. Why might you use the exponential function rather than the quadratic function?Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 1. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that Graph means Graph by hand.) y=x+4 Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that Graph means Graph by hand.) y=14x Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that Graph means Graph by hand.) y=3x Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that Graph means Graph by hand.) y=53x+3 Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that Graph means Graph by hand.) y=23x4 Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 7. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 8. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 9. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that Graph means Graph by hand.) 8y2x=4 Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 11. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 12. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 13. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 14. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that Graph means Graph by hand.) x=y2+2 Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 16. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 17. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that Graph means Graph by hand.) y=|x|Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that Graph means Graph by hand.) y=7x2 Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 20. Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that Graph means Graph by hand.) y7=x3 Exercises designated by the symbol are Thinking and Writing Exercises. They should be answered using one or two English sentences. Because answers to many such exercises will vary, solutions are not given at the back of the book. Graph. (Unless directed otherwise, assume that “Graph” means “Graph by hand”.) 22. Medicine. Ibuprofen is a medication used to relieve pain. The function A=0.5t4+3.45t396.65t2+347.7t,0t6, can be used to estimate the number of milligrams, A, of Ibuprofen in the bloodstream t hours after 400 mg of the medication has been swallowed. (Source: Based on data from Dr. P. Carey, Burlington, VT.) How many milligrams of Ibuprofen are in the bloodstream 2 hr after 400 mg has been swallowed?24. Running records. According to at least one study, the world record in any running race can be modeled by a linear equation. In particular, the world record R, in minutes, for the mile run in year x can be modeled by Use this model to estimate the world records for the mile run in 1954, 2000, and 2015. Round your answers to the nearest hundredth of a minute. 25. Snowboarding in the half-pipe. Shaun White, “The Flying Tomato,” won a gold medal in the 2010 Winter Olympics for snowboarding in the half-pipe. He soared an unprecedented 25 ft above the edge of the half-pipe. His speed in miles per hour, upon reentering the pipe can be approximately by where t is the number of seconds for which he was airborne. White was airborne for 2.5 sec. (Source: “White Rides to Repeat in Halfpipe, Lago Takes Bronze,” Associated Press, 2/18/2010.) How fast was he going when he reentered the half-pipe? 26. Skateboard bomb drop. The distance in feet, traveled by a body falling freely from rest in t seconds is approximated by On April 6, 2006, pro skateboarder Danny Way smashed the world record for the “bomb drop” by free-falling 28 ft from the Fender Stratocaster guitar atop the Hard Rock Hotel & Casino in Las Vegas onto a ramp below. (Source: www.skateboardingmagazine.com.) How long did it take until he hit the ramp? Hearing-impaired Americans. The number N, in millions, of hearing-impaired Americans of age x can be approximated by the graph that follows. Use the graph to answer the following. a. Approximate the number of hearing-impaired Americans of ages 20, 40, 50, and 60. b. For what ages is the number of hearing-impaired Americans approximately 4 million? c. Estimate the age for which the greatest number of Americans is hearing-impaired. d. What difficulty do you have in making this determination?Life Science: incidence of breast cancer. The following graph approximates the incidence of breast cancer y, per 100,000 women, as a function of age x, where x represents ages 25 to 102. a. What is the incidence of breast cancer in 40-yr-old women? b. For what ages is the incidence of breast cancer about 400 per 100,000 women? c. Examine the graph and try to determine the age at which the largest incidence of breast cancer occurs. d. What difficulty do you have making this determination?Compound Interest. Southside investments purchases a $100,000 certificate of deposit from Newton Bank, at 2.8%. How much is the investment worth (rounded to the nearest cent) at the end of 1 yr, if interest is compounded: a. Annually? b. Semiannually? c. Quarterly? d. Daily (use 365 days for 1 yr) e. Hourly?30. Compounded Interest. Greenleaf Investments purchases a $300,000 certificate of deposit from Descartes Bank, at 2.2%. How much is the investment worth (rounded to the nearest cent) at the end of 1 yr, if interest is compounded: a. Annually? b. Semiannually? c. Quarterly? d. Daily (use 365 days for 1 yr)? e. Hourly? 31. Compounded Interest. Stateside Brokers deposit $30,000 in Godel Municipal Bond Funds, at 4%. How much is the investment worth (rounded to the nearest cent) at the end of 3 yr, if interest is compounded: a. Annually? b. Semiannually? c. Quarterly? d. Daily (use 365 days for 1 yr)? e. Hourly? Compounded Interest. The Kims deposit $1000 in Wiles Municipal Bond Funds, at 5%. How much is the investment worth (rounded to the nearest cent) at the end of 4 yr, if interest is compounded: a. Annually? b. Semiannually? c. Quarterly? d. Daily (use 365 days for 1 yr) e. Hourly?If P dollars are borrowed at an annual interest rate r, the payment M made each month for a total of n months is M=Pr12(1+r12)n(1+r12)n1. Fermats Last Bank makes a car loan of $18,000, at 6.4% interest and with a loan period of 3 yr. What is the monthly payment?If P dollars are borrowed at an annual interest rate r, the payment M made each month for a total of n months is . 34. At Haken Bank, Ken Appel takes out a $100,000 mortgage at an interest rate of 4.8% for a loan period of 30 yr. What is the monthly payment? If P dollars are invested annually in an annuity (investment fund), after n years, the annuity will be worth W=P[(1+r)n1r], where r is the interest rate, compounded annually. Kate invests $3000 annually in an annuity from Mersenne Fund that earns 6.57% interest. How much is the investment worth after 18 yr? Round to the nearest cent.If P dollars are invested annually in an annuity (investment fund), after n years, the annuity will be worth W=P[(1+r)n1r], where r is the interest rate, compounded annually. Paulo establishes an annuity that earns 714 interest and wants it to be worth $50,000 in 20 yr. How much will he need to invest annually to achieve this goal?37. Condor population. The condor population in California and Arizona from 2002 to 2012 is approximated in the graph below. a. In what years was the condor population at or above 230? b. In what year was the condor population at 200? c. In what year was the condor population the highest? d. In what year was the condor population the lowest? Speculate as to why the condor population in Calfornia and Arizona experienced such a dramatic rise in 2007-2008.Sally makes deposits into a retirement account every year from the age of 30 until she retires at age 65. a. If Sally deposits $1200 per year and the account earns interest at a rate of 4% per year, compounded annually, how will she have in the account when she retires? (Hint: Use the annuity formula given for Exercises 35 and 36.) b. How much of that total amount is from Sallys deposits? How much is interest?Sally makes deposits into a retirement account every year from the age of 30 until she retires at age 65. 40. a. Sally plans to take regular monthly distributions from her retirement account from the time she retires until she is 80 years old, when the account will have a value of $0. How much should she take each month? Assume the interest rate is 4% per year, compounded monthly. (Hint: Use the formula given for Exercises 33 and 34 that calculates the monthly payments on a loan.) b. What is the total of the payments she will receive? How much of the total will be her own money (see part b of Exercise 39), and how much will be interest? The annual interest rate r, when compounded more than once a year, results in a slightly higher yearly interest rate; this is called the annual (or effective) yield and denoted as Y. For example, $1000 deposited at 5%, compounded monthly for 1 yr (12 months), will have a value of A=1000(1+0.0512)12=1051.16. The interest earned is $51.16/$1000, or 0.05116, which is 5.116% of the original deposit. Thus, we say this account has a yield of Y=0.05116, or 5.116%. The formula for annual yield depends on the annual interest rate r and the compounding frequency n: Y=(1+rn)n1. For Exercises 41-48, find the annual yield as a percentage, to two decimal places, given the annual interest rate and the compounding frequency. Annual interest rate of 5.3%, compounded monthly The annual interest rate r, when compounded more than once a year, results in a slightly higher yearly interest rate; this is called the annual (or effective) yield and denoted as Y. For example, $1000 deposited at 5%, compounded monthly for 1 yr (12 months), will have a value of . The interest earned is $51.16/$1000, or 0.05116, which is 5.116% of the original deposit. Thus, we say this account has a yield of , or 5.116%. The formula for annual yield depends on the annual interest rate r and the compounding frequency n: . For Exercises 41-48, find the annual yield as a percentage, to two decimal places, given the annual interest rate and the compounding frequency. 42. Annual interest rate of 4.1%, compounded quarterly The annual interest rate r, when compounded more than once a year, results in a slightly higher yearly interest rate; this is called the annual (or effective) yield and denoted as Y. For example, $1000 deposited at 5%, compounded monthly for 1 yr (12 months), will have a value of A=1000(1+0.0512)12=1051.16. The interest earned is $51.16/$1000, or 0.05116, which is 5.116% of the original deposit. Thus, we say this account has a yield of Y=0.05116, or 5.116%. The formula for annual yield depends on the annual interest rate r and the compounding frequency n: Y=(1+rn)n1. For Exercises 41-48, find the annual yield as a percentage, to two decimal places, given the annual interest rate and the compounding frequency. Annual interest rate of 3.75%, compounded weekly The annual interest rate r, when compounded more than once a year, results in a slightly higher yearly interest rate; this is called the annual (or effective) yield and denoted as Y. For example, $1000 deposited at 5%, compounded monthly for 1 yr (12 months), will have a value of A=1000(1+0.0512)12=1051.16. The interest earned is $51.16/$1000, or 0.05116, which is 5.116% of the original deposit. Thus, we say this account has a yield of Y=0.05116, or 5.116%. The formula for annual yield depends on the annual interest rate r and the compounding frequency n: Y=(1+rn)n1. For Exercises 41-48, find the annual yield as a percentage, to two decimal places, given the annual interest rate and the compounding frequency. Annual interest rate of 4%, compounded daily The annual interest rate r, when compounded more than once a year, results in a slightly higher yearly interest rate; this is called the annual (or effective) yield and denoted as Y. For example, $1000 deposited at 5%, compounded monthly for 1 yr (12 months), will have a value of A=1000(1+0.0512)12=1051.16. The interest earned is $51.16/$1000, or 0.05116, which is 5.116% of the original deposit. Thus, we say this account has a yield of Y=0.05116, or 5.116%. The formula for annual yield depends on the annual interest rate r and the compounding frequency n: Y=(1+rn)n1. For Exercises 41-48, find the annual yield as a percentage, to two decimal places, given the annual interest rate and the compounding frequency. Lena is considering two savings accounts: Western Bank offers 4.5%, compounded annually, on saving accounts, while Commonwealth Savings offers 4.43%, compounded monthly. a. Find the annual yield for both accounts. b. Which account has the higher annual yield?The annual interest rate r, when compounded more than once a year, results in a slightly higher yearly interest rate; this is called the annual (or effective) yield and denoted as Y. For example, $1000 deposited at 5%, compounded monthly for 1 yr (12 months), will have a value of A=1000(1+0.0512)12=1051.16. The interest earned is $51.16/$1000, or 0.05116, which is 5.116% of the original deposit. Thus, we say this account has a yield of Y=0.05116, or 5.116%. The formula for annual yield depends on the annual interest rate r and the compounding frequency n: Y=(1+rn)n1. For Exercises 41-48, find the annual yield as a percentage, to two decimal places, given the annual interest rate and the compounding frequency. Chris is considering two savings accounts: Sierra Savings offers 5%, compounded annually, on savings accounts, while Foothill Bank offers 4.88%, compounded weekly. a. Find the annual yield for both accounts. b. Which account has the higher annual yield?The annual interest rate r, when compounded more than once a year, results in a slightly higher yearly interest rate; this is called the annual (or effective) yield and denoted as Y. For example, $1000 deposited at 5%, compounded monthly for 1 yr (12 months), will have a value of . The interest earned is $51.16/$1000, or 0.05116, which is 5.116% of the original deposit. Thus, we say this account has a yield of , or 5.116%. The formula for annual yield depends on the annual interest rate r and the compounding frequency n: . For Exercises 41-48, find the annual yield as a percentage, to two decimal places, given the annual interest rate and the compounding frequency. 47. Stockman’s Bank will pay 4.2%, compounded annually, on a savings account. A competitor, Mesalands Savings, offers monthly compounding on savings accounts. What is the minimum annual interest rate that Mesalands needs to pay to make its annual yield exceed that of Stockman’s? The annual interest rate r, when compounded more than once a year, results in a slightly higher yearly interest rate; this is called the annual (or effective) yield and denoted as Y. For example, $1000 deposited at 5%, compounded monthly for 1 yr (12 months), will have a value of . The interest earned is $51.16/$1000, or 0.05116, which is 5.116% of the original deposit. Thus, we say this account has a yield of , or 5.116%. The formula for annual yield depends on the annual interest rate r and the compounding frequency n: . For Exercises 41-48, find the annual yield as a percentage, to two decimal places, given the annual interest rate and the compounding frequency. 48. Belltown Bank offers a certificate of deposit at 3.75%, compounded annually. Shea Savings offers savings accounts with interest compounded quarterly. What is the minimum annual interest rate that Shea needs to pay to make its annual yield exceed that of Belltown? The Technology Connection heading indicates exercises designed to provide practice using a calculator. Graph. 49. The Technology Connection heading indicates exercises designed to provide practice using a calculator. Graph. y=25|x|The Technology Connection heading indicates exercises designed to provide practice using a calculator. Graph. y=x3+2x24x13 The Technology Connection heading indicates exercises designed to provide practice using a calculator. Graph. y=237x The Technology Connection heading indicates exercises designed to provide practice using a calculator. Graph. 9.6x+4.2y=100 The Technology Connection heading indicates exercises designed to provide practice using a calculator. Graph. y=2.3x2+4.8x9 The Technology Connection heading indicates exercises designed to provide practice using a calculator. Graph. 55. The Technology Connection heading indicates exercises designed to provide practice using a calculator. Graph. 56. Note: A review of algebra can be found in Appendix A on p. 585 Determine whether each correspondence is a function. 1. Note: A review of algebra can be found in Appendix A on p. 585 Determine whether each correspondence is a function.Note: A review of algebra can be found in Appendix A on p. 585 Determine whether each correspondence is a function.Note: A review of algebra can be found in Appendix A on p. 585 Determine whether each correspondence is a function.Note: A review of algebra can be found in Appendix A on p. 585 Determine whether each correspondence is a function. Sandwich Prices.Note: A review of algebra can be found in Appendix A on p. 585 Determine whether each correspondence is a function. 6. Sandwich Calorie Content. Determine whether each of the following is a function. Domain Correspondence Range A set of iPods Each iPods memory in gigabytes A set of numbers Determine whether each of the following is a function. Domain Correspondence Range A set of iPods Each iPods serial number A set of alphanumeric codes Determine whether each of the following is a function. 9. Domain Correspondence Range A set of iPods The number of songs on each iPod A set of numbers Determine whether each of the following is a function. 10. Domain Correspondence Range A set of iPods The number of Avril Lavigne songs on each iPod A set of numbers Determine whether each of the following is a function. 11. Domain Correspondence Range The set of all real numbers The square of a number, to which 8 is added The set of all positive numbers greater than or equal to 8 Determine whether each of the following is a function. Domain Correspondence Range The set of all real numbers The fourth power of a number The set of all nonnegative numbers Determine whether each of the following is a function. 13. Domain Correspondence Range A set of females Each person’s biological mother A set of females Determine whether each of the following is a function. 14. Domain Correspondence Range A set of males Each person’s biological father A set of males Determine whether each of the following is a function. 15. Domain Correspondence Range A set of avenues An intersecting road A set of cross streets Determine whether each of the following is a function. Domain Correspondence Range A set of textbooks An even-numbered page in each book A set of pages Determine whether each of the following is a function. Domain Correspondence Range A set of shapes The area of each shape A set of area measurements Determine whether each of the following is a function. Domain Correspondence Range A set of shapes The perimeter of each shape A set of length measurements 19. A function f is given by . This function takes a number x, multiple it by 4, and subtracts 3. a. Complete this table. x 5.1 5.01 5.001 5 17.4 17.04 17.004 17 b. Find and . A function f is given by f(x)=3x+2 This function takes a number x, multiples it by 3, and adds 2. Complete this table. x 4.1 4.01 4.001 4 f(x) 14.3 14.03 14.003 14 b. Find f(5),f(1),f(k),f(1+t), and f(x+h).A function g is given by g(x)=x23. This function takes a number x, squares it, and subtracts 3. Find g(1),g(0),g(1),g(5),g(u),g(a+h), and g(a+h)g(a)h.A function g is given by g(x)=x2+4. This function takes a number x, squares it, and adds 4. Find g(3),g(0),g(1),g(7),g(v),g(a+h), and g(a+h)g(a)h.A function f is given by f(x)=1(x+3)2. This function takes a number x, adds 3, squares the result, and takes the reciprocal of that result. a. Find f(4),f(0),f(a),f(t+4),f(x+h), and f(x+h)f(x)h. b. Note that f could also be given by f(x)=1x2+6x+9. Explain what this does to an input number x.A function f is given by f(x)=1(x5)2. This function takes a number x, subtracts 5 from it, squares the result, and takes the reciprocal of the square. a. Find f(3),f(1),f(k),f(t1),f(t4), and f(x+h). b. Note that f could also be given by f(x)=1x210x+25. Explain what this does to an input number x.A function f takes a number x, multiples it by 4, and adds 2. a. Write f as an equation. f(x)=4x+2 b. Graph f.A function g takes a number x, multiples it by 3, and subtracts 4. a. Write g as an equation. g(x)=3x4 b. Graph g.27. A function h takes a number x. squares it, and adds x. a. Write h as an equation. b. Graph h. 28. A function k takes a number x, squares it, and subtracts 3 times x. a. Write k as an equation. b. Graph k. Graph each function. f(x)=2x5 Graph each function. f(x)=3x1 Graph each function. 31. Graph each function. 32. Graph each function. 33. Graph each function. 34. Graph each function. f(x)=6x2 Graph each function. g(x)=x2+1 Graph each function. 37. Graph each function. 38. Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.) 39. Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.) 40. Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.) 41. Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.)Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.) 43. Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.)Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.)Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.) 46. Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.)Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.)Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.)Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.)Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.) 51. Use the vertical-line test to determine whether each graph is that of a function. (In Exercises 47-50 and 52, the dashed lines are not part of the graphs.) 52. 53. a. Graph . b. Is this a function? a. Graph x=y23. b. Is this a function?55. For , find . 56. For , and . For Exercises 57-60, Consider the function f given by f(x)={2x+1,forx017,forx=0x23,for0x4,12x+1,forx4 Find f(1) and f(1).For Exercises 57-60, Consider the function f given by 58. Find and . For Exercises 57-60, Consider the function f given by f(x)={2x+1,forx017,forx=0x23,for0x4,12x+1,forx4 Find f(0) and f(10).For Exercises 57-60, Consider the function f given by 60. Find and . Graph. f(x)={1,forx0,1,forx0 Graph. 62. Graph. f(x)={6,forx3,6,forx=2,Graph. f(x)={5,forx=1,x3,forx=1,Graph. 65. Graph. 66. Graph. 67. Graph. 68. Graph. f(x)={7,forx=2,x23,forx2 Graph. f(x)={6,forx=3,x2+5,forx3 The amount of money, A(t), in a savings account that pay 3% interest, compounded quarterly for t years, with an initial investment of P dollars, is given by A(t)=P(1+0.034)4t. If $500 is invested at 3%, compounded quarterly, how much will the investment be worth after 2 yr?The amount of money, A(t), in a savings account that pay 3% interest, compounded quarterly for t years, with an initial investment of P dollars, is given by A(t)=P(1+0.034)4t. If $800 is invested at 3%, compounded quarterly, how much will the investment be worth after 3 yr?In computing the dosage for chemotherapy, the measure of a patient’s body surface area is needed. A good approximation of this area, in square meters , is given by where w is the patient’s weight in kilograms (kg) and h is the patient’s height in centimeters (cm). (Source: U.S. Oncology.) Use this information for Exercises 73 and 74. Round your answers to the nearest thousandth. 73. Assume that a patient’s height is 170 cm. Find the patient’s approximate surface area assuming that: a. The patient’s weight is 70 kg. b. The patient’s weight is 100 kg. c. The patient’s weight is 50 kg. In computing the dosage for chemotherapy, the measure of a patients body surface area is needed. A good approximation of this area, in square meters (m2), is given by s=hw3600, where w is the patients weight in kilograms (kg) and h is the patients height in centimeters (cm). (Source: U.S. Oncology.) Use this information for Exercises 73 and 74. Round your answers to the nearest thousandth. Assume that a patients weight is 70 kg. Approximate the patients surface area assuming that: a. The patients height is 150 cm. b. The patients height is 180 cm.Scaling stress factors. In psychology a process called scaling is used to attach numerical ratings to a group of life experiences. In the following table, various events have been rated on a scale from 1 to 100 according to their stress levels. Event Scale of Impact Death of spouse 100 Divorce 73 Jail term 63 Marriage 50 Lost job 47 Pregnancy 40 Death of close friend 37 Loan over $10,000 31 Child leaving home 29 Change in schools 20 Loan less than $10,000 17 Christmas 12 Source: Thomas H. Holmes, University of Washington School of Medicine.) Yes; a unique scale of impact number is assigned to each event. a. Does the table represent a function? Why or why not? b. What are the inputs? What are the outputs?Solve for y in terms of x, and determine if the resulting equation represents a function. 76. Solve for y in terms of x, and determine if the resulting equation represents a function. 2y2+3x=4x+5 Solve for y in terms of x, and determine if the resulting equation represents a function. (4y2/3)3=64x Solve for y in terms of x, and determine if the resulting equation represents a function. (3y3/2)2=72x Explain why the vertical-line test works.81. Is 4 in the domain of f in Exercises 57–60? Explain why or why not. In Exercises 82 and 83, use the table feature to construct a table for the function under the given conditions. f(x)=x3+2x24x13;TblStart=3;Tbl=2 In Exercises 82 and 83, use the table feature to construct a table for the function under the given conditions. 83. A function f is given by f(x)=|x2|+|x+1|5. Find f(3),f(2),f(0), and f(4).Graph the function in each of Exercises 8284.86. A function f takes a number x, adds 2, and then multiplies the result by 5, while a function g takes a number x, multiplies it by 5, and then adds 2. a. Write f and g as equations. b. Graph f and g on the same axes. c. Are f and g the same function? 87. A function f takes a number x, adds 2, and then multiplies the result by 5, while a function g takes a number x, multiplies it by 5, and then adds 2. a. Write f and g as equations. b. Graph f and g on the same axes. c. Are f and g the same function? 88. A function h takes a number x, subtracts 4, and then squares the result, while a function k takes a number x, squares it, and then subtracts 4. a. Write h and k as equations. b. Graph h and k on the same axes. c. Are h and k the same function? 89. A function f takes a number x, multiplies it by 3, and then adds 6, while a function g takes a number x, adds a to it, and then multiplies the result by 3. Find a if f and g are the same function. A function h takes a number x, adds 3, and then squares the result, while a function k takes a number x, squares it, adds 6 times x, and then adds a to the result. Find a if h and k are the same function.1E 2E 3E 4E 5E 6E 7E 8E 9E 10E Write interval notation for each of the following. Then graph the interval on a number line. 11. The set of all numbers x such that. Write interval notation for each of the following. Then graph the interval on a number line. 12. The set of all numbers x such that. Write interval notation for each of the following. Then graph the interval on a number line. {x6x20}Write interval notation for each of the following. Then graph the interval on a number line. {x4x1}Write interval notation for each of the following. Then graph the interval on a number line. 15. Write interval notation for each of the following. Then graph the interval on a number line. 16. Write interval notation for each of the following. Then graph the interval on a number line. {x2x3}Write interval notation for each of the following. Then graph the interval on a number line. {x10x4}Write interval notation for each of the following. Then graph the interval on a number line. {xx12.5}Write interval notation for each of the following. Then graph the interval on a number line. {xx12.5}In Exercises 21 32, each graph is that of a function. Determine (a) f(1); (b) the domain, (c) all x-values such that f(x)=2; and (d) the range.In Exercises 21 – 32, each graph is that of a function. Determine (a) (b) the domain, (c) all x-values such that and (d) the range. 22. In Exercises 21 32, each graph is that of a function. Determine (a) f(1); (b) the domain, (c) all x-values such that f(x)=2; and (d) the range.In Exercises 21 – 32, each graph is that of a function. Determine (a) (b) the domain, (c) all x-values such that and (d) the range. 24. In Exercises 21 – 32, each graph is that of a function. Determine (a) (b) the domain, (c) all x-values such that and (d) the range. 25. In Exercises 21 32, each graph is that of a function. Determine (a) f(1); (b) the domain, (c) all x-values such that f(x)=2; and (d) the range.In Exercises 21 – 32, each graph is that of a function. Determine (a) (b) the domain, (c) all x-values such that and (d) the range. 27. In Exercises 21 – 32, each graph is that of a function. Determine (a) (b) the domain, (c) all x-values such that and (d) the range. 28. In Exercises 21 32, each graph is that of a function. Determine (a) f(1); (b) the domain, (c) all x-values such that f(x)=2; and (d) the range.In Exercises 21 – 32, each graph is that of a function. Determine (a) (b) the domain, (c) all x-values such that and (d) the range. 30. In Exercises 21 – 32, each graph is that of a function. Determine (a) (b) the domain, (c) all x-values such that and (d) the range. 31. In Exercises 21 32, each graph is that of a function. Determine (a) f(1); (b) the domain, (c) all x-values such that f(x)=2; and (d) the range.Find the domain of each function given below. 33. Find the domain of each function given below. f(x)=2x+3 Find the domain of each function given below. 35. Find the domain of each function given below. 36. Find the domain of each function given below. f(x)=x22x+3 Find the domain of each function given below. f(x)=x2+3 Find the domain of each function given below. 39. Find the domain of each function given below. f(x)=83x6 Find the domain of each function given below. 41. Find the domain of each function given below. f(x)=|x|4 Find the domain of each function given below. f(x)=3x172x Find the domain of each function given below. 44. Find the domain of each function given below. g(x)=4+5x Find the domain of each function given below. g(x)=23x Find the domain of each function given below. g(x)=x22x+1 Find the domain of each function given below. 48. Find the domain of each function given below. 49. (Hint: Factor the denominator.) Find the domain of each function given below. 50. (Hint: Factor the denominator.) Find the domain of each function given below. 51. Find the domain of each function given below. g(x)=|x+7|Find the domain of each function given below. g(x)=2x6x26x+5 Find the domain of each function given below. g(x)=3x10x24x5 55. For the function f shown to the right, find all x-values for which. 56. For the function g shown to the right, find all x-values for which. Compound Interest. Suppose $5000 is invested at 3.1% interest, compounded semiannually, for t years. a. The amount A in the account is a function of time Find an equation for this function. A(t)=5000(1+0.0312)2t b. Determine the domain of A.58. Compound Interest. Suppose $3000 is borrowed as a college loan, at 5% interest compounded daily, for t years. a. The amount A that is owed is a function of time. Find an equation for this function. b. Determine the domain of A. Incidence of breast cancer. The following graph (considered in Exercise 28 of Exercise Set R.1 without an equation) approximates the incidence of breast cancer I, per 100,000 women, as a function of age x. The equation for this graph is I(x)=0.0000554x4+0.0067x30.0997x20.84x0.25 (Source: Based on data from the National Cancer Institute) a. Use the graph to determine the domain of I. b. Use the graph to determine the range of I. c. What 10-yr age interval sees the greatest increase in the incidence of breast cancer? Explain how you determined this. d. Approximately [0,455]Hearing-impaired Americans. The following graph (considered in Exercise Set R.1) approximates the number N, in millions, of hearing-impaired Americans who are x years old. The equation for this graph is N(x)=0.000065x3+0.0072x20.133x+2.062. (Source: Better Hearing Institute) a. Use the graph to determine the domain of N. b. Use the graph to determine the range of N. c. If you were marketing a new type of hearing aid, at what age group (expressed as a 10-yr interval) would you target advertisements? Why?Lung cancer. The following graph approximates the incidence of lung and bronchus cancer L, per 100,000 males, as a function of t, the number of years since 1940. The equation for this graph is L(t)=0.00054t3+0.02917t2+1.2329t+8. (Source: Based on data from the American Cancer Society Surveillance Research, 2005.) a. Use the graph to estimate the domain of L. b. Use the graph to estimate the range of L.

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