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32. In a healthy person of height.x inches, the average pulse rate in beats per minute is modeled by the formula 596 P(x) = 30 < x < 100 a. Compute the sensitivity of Pat x = 60. b. Use your answer to part a to estimate the change in pulse rate that corresponds to a height change from 59 to 60 inches. c. Compute the elasticity of P. Does it depend on x?

32. In a healthy person of height.x inches, the average pulse rate in beats per minute is modeled by the formula 596 P(x) = 30 < x < 100 a. Compute the sensitivity of Pat x = 60. b. Use your answer to part a to estimate the change in pulse rate that corresponds to a height change from 59 to 60 inches. c. Compute the elasticity of P. Does it depend on x?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 32

250 Chapter 3 Derivative Rules and Tools a. Compute the elasticity of E(T) at T = 30. b. If the temperature is increased by 5% from 30°C, estimate the corresponding percentage change in Е(T). 36. The gross U.S. federal debt (in trillions of dollars) from 2000 to 2004 is given in the following table Year Gross federal debt 32. In a healthy person of height x inches, the average pulse rate in beats per minute is modeled by the 2000 5.629 2001 5.770 formula 2002 6.198 2003 6.760 596 P(x) = 2004 7.355 30 < x < 100 Data source: From the historical tables of the Office of Manage- ment and Budget, 2006, as downloaded from www.whitehouse. gov/omb/budget/Historicals. a. Compute the sensitivity of Pat x = 60. b. Use your answer to part a to estimate the change in pulse rate that corresponds to a height change from 59 to 60 inches. a. Plot the data and the linear approximation of the data at t = 0 (2000). Discuss the quality of this approximation. c. Compute the elasticity of P. Does it depend on x? b. Use a linear approximation to estimate the federal debt in 2010. Look the actual gross up d. Determine how accurate the measurement of x federal debt to see how well the approximation needs to be to ensure the estimate for P has an worked. error of less than 10%. 37. In Example 7 of Section 2.6, the function 33. In Example 6, we showed that the half-life, T, of a drug with clearance rate x is given by S(t) = 7.292 +0.023t – 0.004t² In 2 was used to fit data on the extent of the Arctic sea ice S (million square kilometers) as a function of years t since 1980 (corresponding to t = 0). = (x)L Suppose that the true value of the clearance rate of some drug is given by x = a. a. What is the sensitivity of S in 1980? b. How has the sensitivity changed from 1980 to 2000? Does this make sense? If not, why not? a. Find the elasticity of T with respect to x. b. If you want to estimate the half-life of this drug within an error of 2%, how accurately do you have to measure the clearance rate of the drug? 38. Consider a power function f(x) = axb with a > 0 and b + 0. Show that the elasticity of f(x) is inde- pendent of the value x. What does it depend on? Ise this answerto quickl solve the following
Transcribed Image Text:250 Chapter 3 Derivative Rules and Tools a. Compute the elasticity of E(T) at T = 30. b. If the temperature is increased by 5% from 30°C, estimate the corresponding percentage change in Е(T). 36. The gross U.S. federal debt (in trillions of dollars) from 2000 to 2004 is given in the following table Year Gross federal debt 32. In a healthy person of height x inches, the average pulse rate in beats per minute is modeled by the 2000 5.629 2001 5.770 formula 2002 6.198 2003 6.760 596 P(x) = 2004 7.355 30 < x < 100 Data source: From the historical tables of the Office of Manage- ment and Budget, 2006, as downloaded from www.whitehouse. gov/omb/budget/Historicals. a. Compute the sensitivity of Pat x = 60. b. Use your answer to part a to estimate the change in pulse rate that corresponds to a height change from 59 to 60 inches. a. Plot the data and the linear approximation of the data at t = 0 (2000). Discuss the quality of this approximation. c. Compute the elasticity of P. Does it depend on x? b. Use a linear approximation to estimate the federal debt in 2010. Look the actual gross up d. Determine how accurate the measurement of x federal debt to see how well the approximation needs to be to ensure the estimate for P has an worked. error of less than 10%. 37. In Example 7 of Section 2.6, the function 33. In Example 6, we showed that the half-life, T, of a drug with clearance rate x is given by S(t) = 7.292 +0.023t – 0.004t² In 2 was used to fit data on the extent of the Arctic sea ice S (million square kilometers) as a function of years t since 1980 (corresponding to t = 0). = (x)L Suppose that the true value of the clearance rate of some drug is given by x = a. a. What is the sensitivity of S in 1980? b. How has the sensitivity changed from 1980 to 2000? Does this make sense? If not, why not? a. Find the elasticity of T with respect to x. b. If you want to estimate the half-life of this drug within an error of 2%, how accurately do you have to measure the clearance rate of the drug? 38. Consider a power function f(x) = axb with a > 0 and b + 0. Show that the elasticity of f(x) is inde- pendent of the value x. What does it depend on? Ise this answerto quickl solve the following
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