Chapter 9.4, Problem 55E

### Mathematical Applications for the ...

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

Chapter
Section

### Mathematical Applications for the ...

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

# Cost-benefit Suppose that tor a certain city, the cost C, in dollars, of obtaining drinking water that contains p percent impurities (by volume) is given by C = 120 , 000 p − 1200 (a) Find the rate of change of cost with respect to p when impurities account for 10% (by volume).(b) Write a sentence that explains the meaning of your answer in part (a).

(a)

To determine

To calculate: The instantaneous rate of change of cost with respect to p for the cost function C=120000p1200, where p is the percentage impurity and is 10% at the instant.

Explanation

Given Information:

The cost function is C=120000pâˆ’1200, where p is the percentage impurity and is 10% at the instant.

Formula Used:

According to sum rule of derivatives,

If

f(x)=u(x)+v(x)

Then,

fâ€²(x)=uâ€²(x)+vâ€²(x)

According to power rule,

If f(x)=xn, then fâ€²(x)=nxnâˆ’1.

According to constant function rule,

If f(x)=c, then fâ€²(x)=0.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x).

Calculation:

Consider the provided cost function is C=120000pâˆ’1200

(b)

To determine

The interpretation from the instantaneous rate of change of cost with respect to p for the cost function C=120000p1200, where p is the percentage impurity and is 10% at the instant.

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