   Chapter 2.4, Problem 81E

Chapter
Section
Textbook Problem

Toxic Waste A city’s main well was recently found to be contaminated with trichloroethylene, a cancer-causing chemical, as a result of an abandoned chemical dump leaching chemicals into the water. A proposal submitted to city council members indicates that the cost, measured in millions of dollars, of removing x% of the toxic pollutant is given by C ( x ) = 0.5 x 100 − x (0 < x < 100) a. Find the cost of removing 50%. 60%. 70%. 80%. 90%. and 95% of the pollutant. b. Evaluate lim x → 100 0.5 x 100 − x and interpret your result.

(a)

To determine

To Find: The cost of removing 50%, 60%, 70%, 80%, 90% and 95% of the pollutant as per given equation.

Explanation

Given information:

The cost measured in millions of dollars of removing x% toxic pollutant is given by,

C(x)=0.5x100x (1)

Where,

• C(x) is the cost in millions of dollars.
• x is the percentage of toxic pollutant.

Calculation:

Substitute 50 for x in equation (1) to find the value of C(50) .

C(50)=0.5×5010050=2550=0.5

The cost required to remove 50% pollutant is 0.5 millions of dollars.

Substitute 60 for x in equation (1) to find the value of C(60) .

C(60)=0.5×6010060=3040=0.75

The cost required to remove 60% pollutant is 0.75 millions of dollars.

Substitute 70 for x in equation (1) to find the value of C(70) .

C(70)=0.5×7010070=3530=1

(b)

To determine

To find: The limit of the given function.

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