Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
High School Graduates The following table shows the number, in millions, graduating from high school in the United States, in the given year.
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a. Explain in practical terms what
b. Use functional notation to express the number of graduates in
c. Find the average rate of change per year during the period
d. Estimate the value of
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Chapter 1 Solutions
FUNCTIONS AND CHANGE COMBO
- Minimum Wage The table below is taken from the website of the U.S. Department of Labor. It shows the minimum wage for each decade from 1950 to 2010. The figures are adjusted for inflation and expressed in constant 2012 dollars. y=Year m=Minimumwage 1950 7.01 1960 7.59 1970 9.28 1980 8.46 1990 6.66 2000 6.90 2010 7.67 a. Find the value of m(1990). b. Use functional notation to express the minimum wage in 1985. c. Use the table to estimate the minimum wage in 1985. The actual value was 7.09.arrow_forwardMortgage Rates The following table is taken from the website of Freddie Mac. It shows rates for 30-year fixed-rate mortgages since 1970. y=Year r=Mortgagerate 1975 9.05 1980 13.74 1985 12.43 1990 10.13 1995 7.93 2000 8.05 2005 5.87 2010 4.69 2015 3.84 a. Explain in practical terms the meaning of r(2003). b. Use the table to estimate the value of r(2003).arrow_forwardWhat Formulas Mean In Exercises S-25 through S-33, you are asked to relate functional notation to practical explanations of what certain functions mean. Time to Pay Off a Loan The function T(P,r,m) gives the time required to pay off an installment loan of P dollars if the APR is r as a decimal and we make monthly payments of in dollars. Use functional notation to indicate the time required to pay off a 12,000 automobile loan at an APR of 5 if the monthly payment is 450.arrow_forward
- What Formulas Mean In Exercises S-25 through S-33, you are asked to relate functional notation to practical explanations of what certain functions mean. Grocery Bill If c(p,s,h) is the cost of buying p bags of potato chips, ssodas, and h hot dogs, use functional notation to express the cost of buying 2 bags of potato chips, 3 sodas, and 5 hot dogs.arrow_forwardDepreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20000(0.90) and the value of the car after the end of the second year would be $20000(0.90)2. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.arrow_forwardTax Owed According to the Oklahoma Income Tax Table for 2010, the income tax owed by an Oklahoma resident who is married and filing jointly with a taxable income above 100, 000 is 5070 plus 5.5 of the taxable income over 100, 000. a. Use a formula to express the tax owed as a function of the taxable income, assuming that the taxable income is above 100, 000. Be sure to explain the meaning of the letters you choose and the units. b. What is the tax on a taxable income of 108, 650? Round your answer to the nearest dollar. c. For what taxable income would the tax be 5686?arrow_forward
- Falling with a parachute If an average-sized man jumps from an airplane with an open parachute, his downward velocity t seconds into the fall is v(t)=20(10.2t) Feet per second. a. Use functional notation to express the velocity 2 seconds into the fall, and then calculate it. b. Explain how the velocity increases with time. Include in your explanation the average rate of change from the beginning of the fall to the end of the first second and the average rate of change from the fifth second to the sixth second of the fall. c. Find the terminal velocity. d. Compare the time it takes to reach 99 of terminal velocity here with the time it took to reach 99 of terminal velocity in Example 2.1. On the basis of the information we have, which would you expect to reach 99 of terminal velocity first, a feather or a cannonball?arrow_forwardGross Profit Margin The gross profit margin is a measurement of a companys manufacturing and distribution efficiency during the production process. If G is the gross profit and T is the total revenue, both in dollars, then the gross profit margin M=M(G,T) is given by the formula M=GT a. Use functional notation to express the gross profit margin for a company that has a gross profit of 335, 000 and a total revenue of 540, 000. b. Calculate the gross profit margin in part a. The gross profit margin is often expressed as a percent. Give your answer as both a decimal and a percent. c. If the gross profit stays the same but total revenue increases, would the gross profit margin increase or decrease?arrow_forwardLater Public High School Enrollment Here is a model for the number of students enrolled in U.S. public high schools as a function of time since 2000. N=0.033t2+0.46t+13.37 In this formula, N is the enrollment in millions of students, t is the time in years since 2000, and the model is applicable from 2000 to 2010. a. Calculate N(10) and explain in practical terms what it means. b. In what year was the enrollment the largest? c. Find the average yearly rate of change in enrollment from 2004 to 2010. Is the result misleading, considering your answer to part b?arrow_forward
- Growth in Length of Haddock D.S. Raitt found that the length L of haddock in centimeters as a function of the age t in years is given approximately by the formula L=5342.820.82t a. Calculate L(4) and explain what it means. b. Compare the average yearly rate of growth in length from age 5 to age 10 years with the average yearly rate of growth from age 15 to age 20 years. Explain in practical terms what this tells you about the way haddock grow. c. What is the longest haddock you would expect to find anywhere?arrow_forwardReaction Time For certain decisions, the time it takes to respond is a logarithmic function of the number of choices faced. One model is, R=0.17+0.44logN where R is the reaction time in seconds and N is the number of choices. a.Draw a graph of R versus N. Include values of N from 1 to 10 choices. b.Using functional notation, express the reaction if there are seven choices, and then calculate that time. c.If the reaction is to be at most 0.5 second, how many choices can there be? d.If the number of choices increases by a factor of 10, what happens to the reaction time. e.Explain in practical terms what the concavity of graph means.arrow_forwardTitanic At 2:00 p.m. on April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 p.m. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approximately 3400-mile trip. (a) What was the total duration of the voyage in hours? (b) What was the average speed in miles per hour? (c) Write a function relating the distance of the Titanic from New York City and the number of hours traveled. Find the domain and range of the function. (d) Graph the function in part (c).arrow_forward
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