   Chapter 10.5, Problem 36E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Cost-benefit The percent p of impurities that can be removed from the wastewater of a manufacturing process at a cost of C dollars is given by p = 100 C 8100 + C (a) Find any C-values at which the rate of change of p with respect to C does not exist. Make sure that these make sense in the problem.(b) Find C-values for which p is increasing.(c) Find any horizontal asymptotes.(d) Can 100 % of the pollution be removed?

(a)

To determine

To calculate: The value of C at which the rate of change of p with respect to C does not exist for the function p=100C8100+C; where p is the percentage of impurities that can be removed by spending C dollars.

Explanation

Given Information:

The provided function is p=100C8100+C; where p is the percentage of impurities that can be removed by spending C dollars.

Formula used:

According to the quotient rule,

If f(x)=u(x)v(x), then,

ddx(f(x))=(v(x))ddx(u(x))(u(x))ddx(v(x))(v(x))2

Calculation:

First calculate the rate of change of p with respect to C.

Thus, differentiate the function with respect to C.

ddC(p)=ddC(100C8100+C)

Use the quotient rule to differentiate the function,

ddC(p)=ddC(100C8100+C)=(8100+C)ddC(

(b)

To determine

To calculate: The value of C at which p is increasing for the function p=100C8100+C; where p is the percentage of impurities that can be removed by spending C dollars.

(c)

To determine

To calculate: The horizontal asymptote, for the function p=100C8100+C.

(d)

To determine

The explanation if the 100% of impurities can be removed for the function p=100C8100+C; where p is the percentage of impurities that can be removed by spending C dollars.

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