   Chapter 11.4, Problem 88E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Crime Statistics Following is a quadratic model relating the murder rates described in Exercise: y = 0.1 x 2 − 3 x + 39    ( 15 ≤ x ≤ 25 ) , In 1996 the murder rate in smaller cities was approximately 22 murders per 100,000 residents each year and was decreasing at a rate of approximately 2.5 murders per 100,000 residents each year. Use the chain rule to estimate how fast the murder rate was changing for large cities. (Show how you used the chain rule in your answer.)

To determine

To calculate: The speed at which the murder rate dydt was changing in larger cities during 1996 using chain rule if it is given that in 1996 the murder rate in small cities was given by the function y=0.1x23x+39 such that (15x25) and was approximately 22 murders per 100,000 residents each year and was decreasing at a rate of 2.5 murders per 100,000 residents each year.

Explanation

Given Information:

In 1996 the murder rate in small cities was approximately 22 murders per 100,000 residents each year and was decreasing dxdt at a rate of 2.5 murders per 100,000 residents each year and the murder rate is given by the function y=0.1x23x+39 such that (15x25).

Formula used:

Derivative of function y with respect to x using chain rule in differential notation is dydx=dydududx where y is the differential function of u and u is the differential function of x.

Calculation:

Consider that in 1996 the murder rate in small cities was approximately 22 murders per 100,000 residents each year and was decreasing dxdt at a rate of 2.5 murders per 100,000 residents each year and the murder rate is given by the function y=0.1x23x+39 such that (15x25)

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