(a) Explanation Given Information: The provided equation is, C ( t ) = 0.118 t 3 − 2.51 t 2 + 40.2 t + 677 , Where t is the number of years past 2000. Formula Used: The critical values are the only values at which the graph can have turning points, the derivative cannot change sign anywhere except at the critical value. This, in an interval between two critical values, the sign of the derivative at any value in the interval will be the sign of the derivative at all values in the interval. As per the First Derivative Test, The first derivative of the function is evaluated. The first derivative is made equal to zero in order to get the critical points. The values of the critical values are kept inside the original function which gives the critical points. The intervals of the values of x are then evaluated for the relative maximum and minimum. Calculation: Consider the provided equation is C ( t ) = 0.118 t 3 − 2.51 t 2 + 40.2 t + 677 , In order to minimize the sensitivity, the following steps have to followed, Take out the first derivative of the equation by the power rule, C ′ = d d t ( 0.118 t 3 − 2.51 t 2 + 40.2 t + 677 ) = 0.118 d d t ( t 3 ) − 2.51 d d t ( t 2 ) + 40.2 d d t ( t ) + d d t ( 677 ) = 0.354 t 2 − 5.02 t + 40.2 The second derivative is as follows: C ″ = d d t ( 0.354 t 2 − 5 (b) To determine The feature that occurs in the t value obtained in part (a) if C ( t ) = 0.118 t 3 − 2.51 t 2 + 40.2 t + 677 .

MATHMATICAL APPLICATIONS FOR THE MANAGEM

11th Edition

ISBN: 9781305758063

Author: HARSHBARGER

Publisher: CENGAGE C

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Chapter 10, Problem 52RE

(a)

To determine

To calculate: The time at which the rate of change of health care costs per capita reach its minimum if the U.S. per capita cost for health care C can be modeled by C(t)=0.118t3−2.51t2+40.2t+677 where t is the number of years past 2000.

(b)

To determine

The feature that occurs in the t value obtained in part (a) if C(t)=0.118t3−2.51t2+40.2t+677.

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Chapter 10, Problem 51RE

Chapter 10, Problem 53RE

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MATHMATICAL APPLICATIONS FOR THE MANAGEM

Ch. 10.1 - 1. The x- values of critical points are found...Ch. 10.1 - Prob. 2CP Ch. 10.1 - Prob. 3CP Ch. 10.1 - Prob. 4CP Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - 3. Use the graph of in Problem 1 to identify at...Ch. 10.1 - 4. Use the graph of in Problem 2 to identify at...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...

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The time at which the rate of change of health care costs per capita reach its minimum if the U.S. per capita cost for health care C can be modeled by C ( t ) = 0.118 t 3 − 2.51 t 2 + 40.2 t + 677 where t is the number of years past 2000.

Solution Summary: The author explains how the rate of change of health care costs per capita can be modeled by C(t) where t is the number of years past 2000.