Solve the problem.
-Suppose that the cost C of removing p% of the pollutants from a chemical dumping site is given by Can a company afford to remove 100% of the pollutants? Explain.
A) Yes, the cost of removing p% of the pollutants is $400, which is certainly affordable.
B) No, the cost of removing p% of the pollutants is $400, which is a prohibitive amount of money.
C) Yes, the cost of removing p% of the pollutants is $40,000, which is certainly affordable.
D) No, the cost of removing p% of the pollutants increases without bound as p approaches 100.

Question

Solve the problem.
-Suppose that the cost C of removing p% of the pollutants from a chemical dumping site is given by  Can a company afford to remove 100% of the pollutants? Explain.
A) Yes, the cost of removing p% of the pollutants is $400, which is certainly affordable. 
B) No, the cost of removing p% of the pollutants is $400, which is a prohibitive amount of money. 
C) Yes, the cost of removing p% of the pollutants is $40,000, which is certainly affordable. 
D) No, the cost of removing p% of the pollutants increases without bound as p approaches 100.

Quizplus · Accepted Answer

The given cost function is C(p) = 1000(1-e^(-0.05p)). Substituting p=100, we get C(100) = 1000(1-e^(-5)). Since e^(-5) is a very small number, the value of C(100) is very close to 1000, which is a very large and prohibitive cost. Moreover, the cost function increases without bound as p approaches 100, meaning that the cost of removing 100% of the pollutants is not affordable for the company. As p approaches 100, the term inside the square root approaches 0, making the denominator of the fraction nearly equal to 0. This results in the cost increasing without bound, which means that removing 100% of the pollutants is not affordable for the company.

Solve the Problem. -Suppose That the Cost C of Removing P% of the P