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Concept explainers
In Exercises 49–54, assume that a constant rate of change exists for each model formed.
Disney Revenue. The following table lists data regarding revenue from the Disney parks and resorts in 2010 and in 2016.
YEAR, x (in number of years after 2010) |
REVENUE FROM PARKS AND RESORTS (in billions of dollars) |
2010, 0 |
$10.667 |
2016, 6 |
16.974 |
Data: The Disney Company |
a. Use the two data points to find a linear function that fits the data. Let
b. Use the function of part (a) to estimate the revenue in 2014 and to predict the revenue in 2021.
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Chapter 2 Solutions
EBK INTERMEDIATE ALGEBRA
- Insurance Rates The following table gives themonthly insurance rates for a $100,000 life insurancepolicy for smokers 35–50 years of age.a. Create a scatter plot for the data.b. Does it appear that a quadratic function can beused to model the data? If so, find the best-fittingquadratic model.c. Find the power model that is the best fit for the data.d. Compare the two models by graphing each modelon the same axes with the data points. Whichmodel appears to be the better fit?arrow_forwardWorld Military Expenditure The following chart shows total military and arms trade expenditure from 2011–2020 (t = 1 represents 2011). †A bar graph titled "World military expenditure" has a horizontal t-axis labeled "Year since 2010" and a vertical axis labeled "$ (billions)". The bar graph has 10 bars. Each bar is associated with a label and an approximate value as listed below. 1: 1,800 billion dollars 2: 1,775 billion dollars 3: 1,750 billion dollars 4: 1,730 billion dollars 5: 1,760 billion dollars 6: 1,760 billion dollars 7: 1,850 billion dollars 8: 1,900 billion dollars 9: 1,950 billion dollars 10: 1,980 billion dollars (a) If you want to model the expenditure figures with a function of the form f(t) = at2 + bt + c, would you expect the coefficient a to be positive or negative? Why? HINT [See "Features of a Parabola" in this section.] We would expect the coefficient to be positive because the curve is concave up. We would expect the coefficient to be negative because the…arrow_forwardIn Exercises 61–64, find an equation for the level surface of the function through the given point.arrow_forward
- Section 2.4: Chain Rule In Exercises 9–34, find the derivative of the function.arrow_forwardUse this information to solve Exercises 9–11:A company is planning to produce and sell a new line of computers. The fixed cost will be $360,000 and it will cost $850 to produce each computer. Each computer will be sold for $1150. 9. Write the cost function, C, of producing x computers. 10. Write the revenue function, R, from the sale of x computers. 11. Determine the break-even point. Describe what this means.arrow_forwardIn Exercises 1–4, graph the function. State its domain and range.arrow_forward
- . Marriage Rate The marriage rate per 1000 unmarriedwomen for the years 1987–2014 can be modeled bythe function 132x + 1000y = 9570, where x is thenumber of years after 1980. During what year doesthe equation indicate the marriage rate will be 4.29?(Source: National Vital Statistics Report 2010)arrow_forwardIn Exercises 41–48, write a piecewise formula for the function.arrow_forwardExercise 2.2arrow_forward
- The table gives the projections of the population, in millions, of a country's residents over age 16 for selected years from 2015 to 2060. Answer parts (a) through (c). b. What does the model predict that the population will be in 2052? Year 2015 2020 2025 2030 2035 c. In what year does the model predict that the population will be 336.823million? Population (millions) a. Find a linear function that models the data, with y equal to the population in millions and x equal to the number of years after 2010. y=x+ (Type integers or decimals rounded to three decimal places as needed.) 255.161 266.024 276.558 286.967 297,259 Year 2040 2045 2050 2055 2060 Population (millions) 306.634 315.152 323.314 331.770 340.868 Darrow_forwardRetail Sales November and December retail sales,excluding autos, for the years 2001–2010 can be modeled by the function S(x) = -1.751x2 + 38.167x +388.997 billion dollars, where x is the number ofyears after 2000.a. Graph the function for values of x representing2001–2010.b. During what years does the model estimate thesales to be $550 billion?c. The recession in 2008 caused retail sales to drop.Does the model agree with the facts; that is, doesit indicate that a maximum occurred in 2008?arrow_forwardThe figure shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. Use the information in the figure to solve Exercises 67–72. 35,000 30,000 C(x) = 10,000 + 30x 25,000 20,000 15,000 R(x) = 50x 10,000 5000 100 200 300 400 500 600 700 Radios Produced and Sold 67. How many radios must be produced and sold for the company to break even? 68. More than how many radios must be produced and sold for the company to have a profit? 69. Use the formulas shown in the voice balloons to find R(200) – C(200). Describe what this means for the company. 70. Use the formulas shown in the voice balloons to find R(300) – C(300). Describe what this means for the company. 71. a. Use the formulas shown in the voice balloons to write the company's profit function, P, from producing and selling x radios. b. Find the company's profit if 10,000 radios are produced and sold. 72. a. Use the formulas shown in the voice balloons to write the company's profit function,…arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage