Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
The Role of the Coefficient in Power Functions with a Negative Power Consider the family of power functions
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- For the experimental can described in Example 8, write the surface area as a function of (a) the radius r and (b) the height h.arrow_forwardMosteller Formula for Body Surface Area: Body surface area is an important piece of medical information because it is a factor in temperature regulation as well as some drug level determinations. The Mosteller formula gives one way of estimating body surface area B in square meters. The formula uses the weight w in kilograms and the height h in centimeters. The relation is B=hw60 In this exercise, we consider people who are 190 centimeters tall. a. Write a formula for B as a function of w. b. Make a graph of B versus w. includes weights up to 100 kilograms. c. Is the graph you made in part b concave up or concave down? d. In this part, we consider the effect of weight gain on men who are 190 centimeters tall. Would the weight gain have a greater effect on surface area for a lighter man or for a heavier man?arrow_forwardRate of Change for a Linear Function If f is the linear function f=45x, what is the value of dfdx?arrow_forward
- Life Expectancy Versus Health Care Spending One article shows a relationship between per capita health care spending h, in thousands of U.S. dollars per person per year, and life expectancy E, in years. The following formula is adapted from that article: E=72.23+3.85h0.37h2 We should point out that this article includes no justification for the type of model used. a.Plot the graph E versus h. Include spending levels from 1000 to 9000 per person per year so a horizontal span of 1 to 9. b. According to this model, what health care expenditure corresponds to maximum longevity? Round your answer in thousands of dollars per person per year to two decimal places. c.What optimum life expectancy is given by this model? For comparison, in 2011, in the United States, per capita health care spending was 8745 and life expectancy was 78.7 years.arrow_forwardThe table shows the temperatures y (in degrees Fahrenheit) in a city over a 24-hour period. Let x represent the time of day, where x=0 corresponds to 6 a.m. These data can be approximated by the model y=0.026x31.03x2+10.2x+34,0x24. (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit the data? (c) Use the graph to approximate the times when the temperature was increasing and decreasing. (d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period. (e) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?arrow_forwardPrice of Amazons Kindle The following table shows the price of Amazons Kindle 2 e-book reader. It is adapted from data available on the web. Here time is measured in months since February 2009, when the Kindle was launched. Time Price 0 349 5 299 10 249 15 199 a. By calculating differences, show that these data can be modeled using a linear function. b. Find a linear formula that models these data. Be careful about the sign of the slope. c. What price does your formula from part b project for January 2012 35 months after the Kindle was launched? Note: The web data were the basis for speculation that some day the Kindle would be free.arrow_forward
- Swimming Laps Miyuki practices swimming laps with her team. The function y=f(t) graphed below gives her distance in meters from the starting edge of the pool t seconds after she starts her laps. Describe in words Miyukis swim practice. What is her average speed for the first 30 s? Graph the function y=1.2f(t). How is the graph of the new function related to the graph of the original function? What is Miyukis new average speed for the first 30 s?arrow_forwardUse your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.arrow_forwardHigh School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.arrow_forward
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