Explanation Given information: It is provided that an employment research company estimates that the value of a recent MBA graduate to an accounting company is V = 3 e 2 + 5 g 3 where V is the value of graduate, e is the number of years of prior business experience, and g is the graduate school grade-point average. Formula used: The steps for solving the related rate problem are: Step1: List the changing and related quantities followed by restating the problem in rate of change of terms. Step 2: Rewrite the problem using for the changing quantities for their derivatives. Step 3: If possible draw the diagram of the changing quantities and find an equation relating the changing quantities. Step 4: Differentiate with respect to the equation (s) in order to get rate of change in relating quantity. Step 5: Now substitute the values of the provided quantity and their derivative into the derived equation and solve them to get answer. Calculation: Consider the steps of the formula: The changing quantities are V is the value of graduate, e is the number of years of prior business experience, and g is the graduate school grade-point average. Since, the company that currently employs graduates with 3.0 average wishes to maintain a constant employee value of V = 200 but finds the grade point average of its new employees is dropping at a rate of 0.2 per year. Thus, the rate of change of V is 0 at V = 200 , the rate of change of g is − 0.2 when g = 3.0 . Thus, d V d t = 0 when V = 200 , d g d t = − 0.2 when g = 3.0 Since, the rate at which the experience of the new employee must be growing to compensate for the decline in grade point average is to be determined. Thus, What is the rate of change of e Thus, d e d t = ? Consider the provided equation: V = 3 e 2 + 5 g 3 Substitute 200 for V , 3.0 for g in above equation to get: 200 = 3 e 2 + 5 ( 3 ) 3 200 = 3 e 2 + 135 65 3 = e 2 e = 65 3 Thus, e ≈ 4

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Chapter 12.5, Problem 41E

To determine

To calculate: The rate at which the experience of the new employee must be growing to compensate for the decline in grade point average. The company that currently employs graduates with 3.0 average wishes to maintain a constant employee value of V=200 but finds the grade point average of its new employees is dropping at a rate of 0.2 per year.

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Chapter 12.5, Problem 40E

Chapter 12.5, Problem 42E

Chapter 12 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

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Solution Summary: The author calculates the rate at which the experience of the new employee must be growing to compensate for the decline in grade point average.

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