(a) Explanation The function that represents the percent of children taking antidepressants from 2004 to 2009 is given f ( x ) = − 0.085 x + 2.97 , where x is the number of years after 2000. The inverse of the function is evaluated as follows. Replace f ( x ) with y in the function f ( x ) = − 0.085 x + 2.97 and obtain as, y = − 0.085 x + 2.97 . Obtain the value of x in terms of y as, y = − 0.085 x + 2.97 y − 2.97 = − 0.085 x x = − y − 2.97 0.085 Interchange x and y to obtain y = 2.97 − x 0.085 (b) To determine To find: The year at which the percent of children taking antidepressants is 2.3%.

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

5th Edition

ISBN: 9780134179025

Author: Ronald J. Harshbarger, Lisa S. Yocco

Publisher: PEARSON

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Chapter 4.3, Problem 37E

(a)

To determine

To find: The inverse of the function f(x)=−0.085x+2.97 and explain what does the outputs of the inverse function represent.

(b)

To determine

To find: The year at which the percent of children taking antidepressants is 2.3%.

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Chapter 4.3, Problem 36E

Chapter 4.3, Problem 38E

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Chapter 4 Solutions

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The inverse of the function f ( x ) = − 0.085 x + 2.97 and explain what does the outputs of the inverse function represent.

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To find: The inverse of the function f(x)=−0.085x+2.97 and explain what does the outputs of the inverse function represent.

To find: The year at which the percent of children taking antidepressants is 2.3%.

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