   Chapter 9.5, Problem 39E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

Cost-bene fit If the cost C (in dollars) of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by C ( p ) = 8100 p 100 − p find the rate of change of C with respect to p.

To determine

To calculate: The rate of change of C if the cost C (in dollars) of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by C(p)=(8100p)(100p).

Explanation

Given Information:

The provided equation is C(p)=(8100p)(100p).

Formula Used:

As per the quotient rule, if two functions are given in the form f(x)g(x), then the derivative is given as:

ddx(fg)=fggfg2.

The rate is determined by the first derivative of the equation.

Calculation:

Consider the provided equation is C(p)=(8100p)(100p).

In order to take out the rate of the cost with respect to the percent, the following needs to be done,

In the above equation, take,

f(p)=(8100p)

And

g(p)=(100p)

Apply the quotient rule of the equation as,

ddp(fg)=ddp(8100p)(100p)ddp(100p)(8100p)(100p)2

Evaluate the equation further,

ddp(fg)=(ddp(8100p))

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