Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
12th Edition
ISBN: 9780134767628
Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins
Publisher: PEARSON
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Textbook Question
Chapter 4.2, Problem 5E
In each of the following problems, find an exponential function of the form
Office Rent The annual average price per square foot for office space in San Francisco was $30.48 in 2004, and it was $66.71 in 2015. (Data from: San Francisco Business Times.)
Find a model for these data in which
If the model remains accurate, what was the predicted rent per square foot in 2016?
By experimenting with different values (or using a graphing calculator to solve an appropriate equation), estimate the first full year in which the price per square foot exceeded $45.
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The following table gives the monthly premiums for an insurance policy on people of various ages.
a. Find an exponential function that models the monthly
premium as a function of age.
b. Find the quadratic function that is the best fit for the data.
c. Graph each function with the data points to determine
which model is the better fit.
a. The exponential function that models the data is y= 3.059 (1.104*).
(Use integers or decimals rounded to the nearest thousandth as needed for any numbers in the expression.)
b. The quadratic function that models the data is y= 6.188x2-557.818x+12,448.185.
(Use integers or decimals rounded to the nearest thousandth as needed for any numbers in the expression.)
Age
35
40
45
50
55
Monthly
Premium (S)
127
164
242
362
559
Age
60
65
70
75
Full data set
Monthly
Premium (S)
946
1904
3485
5873
Based on the scatterplot and computer output, a
A popular social media platform has begun offering
stock shares to the public. In the past 2 years, the
reasonable estimate for the stock price for week 95 is:
price of the stock has generally increased. An
investment specialist gathers data on the stock price
during the past 2 years and creates an exponential
model for estimating the stock price based on the
number of weeks after the first public offering.
$2.27 because ŷ = 0.0022(95) + 2.0583 = 2.2673.
$9.65 because log y =0.0022(95) +2.0583 =2.2673 and
e2.2673 = 9.6533.
%3D
log(Stock Price) vs. Weeks
$185.05 because log y =0.0022(95) + 2.0583 =2.2673
2.28
and 102.2673 = 185.05.
%3D
2.26
2.24
$220.44 because log y =0.0030(95) + 2.0583 =2.3433 and
2.22
102.3433 = 220.44
8 2.2
à 2.12
2.16
2.14
2.12
2.1
2.08
Mark this and return
Save and Exit
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log(Stock Price)
A popular social media platform has begun offering stock shares to the public. In the past 2 years, the price of the stock has generally increased. An investment specialist gathers data on the stock price during the past 2 years and creates an exponential model for estimating the stock price based on the number of weeks after the first public offering.
Based on the scatterplot and computer output, a reasonable estimate for the stock price for week 95 is:
$2.27 because ŷ = 0.0022(95) + 2.0583 = 2.2673.
$9.65 because and e2.2673 = 9.6533.
$185.05 because and 102.2673 = 185.05.
$220.44 because and 102.3433 = 220.44
Chapter 4 Solutions
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
Ch. 4.1 - Checkpoint 1
(a) Fill in this table:
x g(x) =...Ch. 4.1 - Prob. 2CPCh. 4.1 - Checkpoint 3
Use a graphing calculator to graph ...Ch. 4.1 - Prob. 4CPCh. 4.1 - Checkpoint 5
Graph
Ch. 4.1 - Prob. 6CPCh. 4.1 - Checkpoint 7 Per-person wine consumption (in...Ch. 4.1 - Classify each function as linear, quadratic, or...Ch. 4.1 - Prob. 2ECh. 4.1 - Prob. 3E
Ch. 4.1 - Prob. 4ECh. 4.1 - Classify each function as linear, quadratic, or...Ch. 4.1 - Prob. 6ECh. 4.1 - Without graphing,
(a) describe the shape of the...Ch. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Without graphing,
(a) describe the shape of the...Ch. 4.1 - Prob. 12ECh. 4.1 - Graph each function. (See Examples 1–3.)
13.
Ch. 4.1 - Prob. 14ECh. 4.1 - Graph each function. (See Examples 1–3.)
15.
Ch. 4.1 - Prob. 16ECh. 4.1 - Graph each function. (See Examples 1–3.)
17.
Ch. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - In Exercises 27 and 28, the graph of an...Ch. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - 30. Give a rule of the form to define the...Ch. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - 36. Finance If money loses value at the rate of 3%...Ch. 4.1 - Work these problems. (See Example 5.)
37. Finance...Ch. 4.1 - 38. Natural Science Biologists have found that the...Ch. 4.1 - Work the following exercises.
39. Prudential...Ch. 4.1 - 40. Business The monthly payment on a car loan at...Ch. 4.1 - 41. Natural Science The amount of plutonium...Ch. 4.1 - Business The scrap value of a machine is the value...Ch. 4.1 - Business The scrap value of a machine is the value...Ch. 4.1 - Business The scrap value of a machine is the value...Ch. 4.1 - Work the following problems. (See Examples 5 and...Ch. 4.1 - Work the following problems. (See Examples 5 and...Ch. 4.1 -
GDP Use the following information to answer...Ch. 4.1 -
GDP Use the following information to answer...Ch. 4.1 - GDP Use the following information to answer...Ch. 4.1 -
GDP Use the following information to answer...Ch. 4.1 - Asset Management The amount of money (in trillions...Ch. 4.1 - Imports from Vietnam The value of U.S. imports...Ch. 4.1 -
53. Subprime Mortgages The amount of money (in...Ch. 4.1 - Subprime Mortgages The amount of money (in...Ch. 4.2 - Checkpoint 1
Suppose the number of bacteria in a...Ch. 4.2 - Checkpoint 2
Suppose an investment grows...Ch. 4.2 - Prob. 3CPCh. 4.2 - Prob. 4CPCh. 4.2 - Prob. 1ECh. 4.2 - 2. Finance Suppose you owe $1500 on your credit...Ch. 4.2 - Natural Gas Production Theannual amount of energy...Ch. 4.2 - Oil Production The annual amount of U.S. crude-oil...Ch. 4.2 - In each of the following problems, find an...Ch. 4.2 - 6. Social Science The U.S. Census Bureau predicts...Ch. 4.2 -
In each of the following problems, find an...Ch. 4.2 -
In each of the following problems, find an...Ch. 4.2 - In the following exercises, find the exponential...Ch. 4.2 - Prob. 10ECh. 4.2 - In the following exercises, find the exponential...Ch. 4.2 - In the following exercises, find the exponential...Ch. 4.2 - 13. Business Assembly-line operations tend to have...Ch. 4.2 - 14. Social Science The number of words per minute...Ch. 4.2 - Natural Science Newton's law of cooling says that...Ch. 4.2 - Natural Science Newton's law of cooling says that...Ch. 4.2 - Internet Use in China The percentage of Chinese...Ch. 4.2 - Seat-Belt Use Data form the National Highway...Ch. 4.2 - Food Assistance The amount of money the U.S....Ch. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.3 - Checkpoint 1
Find each common logarithm.
(a) log...Ch. 4.3 - Prob. 2CPCh. 4.3 - Prob. 3CPCh. 4.3 - Prob. 4CPCh. 4.3 - Prob. 5CPCh. 4.3 - Prob. 6CPCh. 4.3 - Prob. 8CPCh. 4.3 - Prob. 1ECh. 4.3 - Complete each statement in Exercises 1–4.
2. The...Ch. 4.3 - Complete each statement in Exercises 1–4.
3. What...Ch. 4.3 - Complete each statement in Exercises...Ch. 4.3 - Translate each logarithmic statement into an...Ch. 4.3 - Translate each logarithmic statement into an...Ch. 4.3 - Translate each logarithmic statement into an...Ch. 4.3 - Translate each logarithmic statement into an...Ch. 4.3 - Translate each exponential statement. into an...Ch. 4.3 - Translate each exponential statement into an...Ch. 4.3 - Translate each exponential statement into an...Ch. 4.3 - Translate each exponential statement into an...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Without using a calculator, evaluate each of the...Ch. 4.3 - Use a calculator to evaluate each logarithm to...Ch. 4.3 - Use a calculator to evaluate each logarithm to...Ch. 4.3 - Use a calculator to evaluate each logarithm to...Ch. 4.3 - Use a calculator to evaluate each logarithm to...Ch. 4.3 - 29. Why does 1 always equal 0 for any valid base...Ch. 4.3 - Prob. 30ECh. 4.3 - Write each expression as the logarithm of a single...Ch. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Write each expression as the logarithm of a single...Ch. 4.3 - Write each expression as the logarithm of a single...Ch. 4.3 - Write each expression as the logarithm of a single...Ch. 4.3 - Write each expression as the logarithm of a single...Ch. 4.3 - Write each expression as a sum and/or a difference...Ch. 4.3 - Write each expression as a sum and/or a difference...Ch. 4.3 - Write each expression as a sum and/or a difference...Ch. 4.3 - Write each expression as a sum and/or a difference...Ch. 4.3 - Write each expression as a sum and/or a difference...Ch. 4.3 - Express each expression in terms of u and v, where...Ch. 4.3 - Express each expression in terms of u and v, where...Ch. 4.3 - Express each expression in terms of u and v, where...Ch. 4.3 - Express each expression in terms of u and v, where...Ch. 4.3 - Evaluate each expression. (See Example 9.)
Example...Ch. 4.3 - Evaluate each expression. (See Example 9.)
Example...Ch. 4.3 - Evaluate each expression. (See Example 9.)
Example...Ch. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - 62. Health Two people with flu visited a college...Ch. 4.3 - Health Insurance Costs The average annual cost (in...Ch. 4.3 - Prob. 64ECh. 4.3 - Dairy Expenditures The average annual expenditures...Ch. 4.3 - Credit Union Assets The total assets (in billions...Ch. 4.3 - Border Patrol Budget The amount (in billions) that...Ch. 4.3 - Opioid Deaths The number of deaths from opioids in...Ch. 4.3 - 69. Apple iPhone Sales The worldwide number (in...Ch. 4.3 - Prob. 70ECh. 4.4 - Checkpoint 1
Solve each equation.
(a)
(b)
Ch. 4.4 - Prob. 2CPCh. 4.4 - Prob. 3CPCh. 4.4 - Prob. 4CPCh. 4.4 - Prob. 5CPCh. 4.4 - Checkpoint 6
Solve each equation. Round solutions...Ch. 4.4 - Prob. 7CPCh. 4.4 - Prob. 8CPCh. 4.4 - Prob. 9CPCh. 4.4 - Prob. 10CPCh. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Prob. 2ECh. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Solve each logarithmic equation. (See Example...Ch. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - 21. Suppose you overhear the following statement:...Ch. 4.4 - Prob. 22ECh. 4.4 - Solve these exponential equations without using...Ch. 4.4 - Solve these exponential equations without using...Ch. 4.4 - Solve these exponential equations without using...Ch. 4.4 - Solve these exponential equations without using...Ch. 4.4 - Solve these exponential equations without using...Ch. 4.4 - Solve these exponential equations without using...Ch. 4.4 - Solve these exponential equations without using...Ch. 4.4 - Solve these exponential equations without using...Ch. 4.4 - Use logarithms to solve these exponential...Ch. 4.4 - Use logarithms to solve these exponential...Ch. 4.4 - Use logarithms to solve these exponential...Ch. 4.4 - Use logarithms to solve these exponential...Ch. 4.4 - Use logarithms to solve these exponential...Ch. 4.4 - Use logarithms to solve these exponential...Ch. 4.4 - Use logarithms to solve these exponential...Ch. 4.4 - Use logarithms to solve these exponential...Ch. 4.4 - Use logarithms to solve these exponential...Ch. 4.4 - Use logarithms to solve these exponential...Ch. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Prob. 45ECh. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - Prob. 50ECh. 4.4 - Prob. 51ECh. 4.4 - Prob. 52ECh. 4.4 - Solve these equations. (See Examples 1–6.)
53.
Ch. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Prob. 56ECh. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - Solve these equations. (See Examples 1−6.)
59.
Ch. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - Work these problems. (See Examples 6, 7, and...Ch. 4.4 - Work these problems. (See Examples 6, 7, and 8.)...Ch. 4.4 - Work these problems. (See Examples 6, 7, and 8.)...Ch. 4.4 - Work these problems. (See Examples 6, 7, and 8.)...Ch. 4.4 - Work these problems. (See Examples 6, 7, and...Ch. 4.4 - Work these problems. (See Examples 6, 7, and 8.)...Ch. 4.4 - Work these problems. (See Examples 6, 7, and...Ch. 4.4 - Work these problems. (See Examples 6, 7, and 8.)...Ch. 4.4 - Work these problems. (See Examples 6, 7, and 8.)...Ch. 4.4 - Work these problems. (See Examples 6, 7, and 8.)...Ch. 4.4 - Work these problems. (See Examples 6, 7, and 8.)...Ch. 4.4 - Work these problems. (See Examples 6, 7, and...Ch. 4.4 - Work these exercises. (See Example 8.)
Example...Ch. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Prob. 78ECh. 4.4 - Prob. 79ECh. 4.4 - Prob. 80ECh. 4.4 - Prob. 81ECh. 4.4 - Prob. 82ECh. 4 - Match each equation with the letter of the graph...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Consider the exponential function y = f(x) = ax...Ch. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Evaluate these expressions without using a...Ch. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Solve each equation. Round to the nearest...Ch. 4 - Solve each equation. Round to the nearest...Ch. 4 - Solve each equation. Round to the nearest...Ch. 4 - Solve each equation. Round to the nearest...Ch. 4 - Solve each equation. Round to the nearest...Ch. 4 - Solve each equation. Round to the nearest...Ch. 4 - Solve each equation. Round to the nearest...Ch. 4 - 48.
Solve each equation. Round to the nearest...Ch. 4 - Prob. 49RECh. 4 - Solve each equation. Round to the nearest...Ch. 4 - Solve each equation. Round to the nearest...Ch. 4 - Solve each equation. Round to the nearest...Ch. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - For Exercises 1–6, use Equation (1) that provides...Ch. 4 - Prob. 2CECh. 4 - For Exercises 16, use Equation (1) that provides a...Ch. 4 - For Exercises 1–6, use Equation (1) that provides...Ch. 4 - For Exercises 1–6, use Equation (1) that provides...Ch. 4 - For Exercises 1–6, use Equation (1) that provides...Ch. 4 - For Exercises 710, use the model in Equation (2)...Ch. 4 - For Exercises 7–10, use the model in Equation (2)...Ch. 4 - For Exercises 7–10, use the model in Equation (2)...Ch. 4 - For Exercises 7–10, use the model in Equation (2)...Ch. 4 - For Exercises 1114, use the model in Equation (3)...Ch. 4 - Prob. 12CECh. 4 - Prob. 13CECh. 4 - For Exercises 11–14, use the model in Equation (3)...Ch. 4 - Prob. 1EPCh. 4 - Prob. 2EPCh. 4 - Prob. 3EP
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