   Chapter 11.4, Problem 87E 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 The murder rate in large cities (over 1 million residents) can be related to that in smaller cities (500,000–1,000,000 residents) by the following linear model: y = 1.5 x − 1.9    ( 15 ≤ x ≤ 25 ) , where y is the murder rate (in murders per 100,000 residents each year) in large cities and x is the murder rate in smaller cities. During the period 1991–1998 the murder rate in small cities was decreasing at an average rate of 2 murders per 100,000 residents each year. Use the chain rule to estimate how fast the murder rate was changing in larger cities during that period. (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 the period 19911998 using chain rule if it is given that the murder rate in large cities (over 1 million residents) can be related to that in smaller cities (500,0001,000,000residents) by the function y=1.5x1.9 such that (15x25) where y is the murder rate in smaller cities and during the period 19911998 and the murder rate dxdt in small cities was decreasing at an average rate of 2 murders per 100,000 residents each year.

Explanation

Given Information:

The murder rate in large cities (over 1 million residents) can be related to that in smaller cities (500,0001,000,000residents) is given by the function y=1.5x1.9 such that (15x25) where y is the murder rate in smaller cities and during the period 19911998 the murder rate dxdt in small cities was decreasing at an average rate of 2 murders per 100,000 residents each year.

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 the function, y=1.5x1

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