The Millcreek watershed area was heavily strip-mined for coal during the late 1960s. Because of the resulting pollution, the streams cannot support fish. Suppose the cost C of obtaining stream water that contains p percent of the current pollution levels is given by . Because p is the percent of current pollution levels, . Use the restriction on p and determine a range for C so that an accurate graph can be obtained with a graphing utility. Describe what happens to the cost as p takes on positive values near 0.
A) Near p = 0, the cost approaches $3,380.
B) Near p = 0, the cost grows without bound.
C) Near p = 0, the cost approaches $338,000.
D) Near p = 0, cost approaches $0.
E) Near p = 0, the cost becomes negative.

Question

The Millcreek watershed area was heavily strip-mined for coal during the late 1960s. Because of the resulting pollution, the streams cannot support fish. Suppose the cost C of obtaining stream water that contains p percent of the current pollution levels is given by  . Because p is the percent of current pollution levels,  . Use the restriction on p and determine a range for C so that an accurate graph can be obtained with a graphing utility. Describe what happens to the cost as p takes on positive values near 0. ​
A) Near p = 0, the cost approaches $3,380. 
B) Near p = 0, the cost grows without bound. 
C) Near p = 0, the cost approaches $338,000. 
D) Near p = 0, cost approaches $0. 
E) Near p = 0, the cost becomes negative.

Quizplus · Accepted Answer

Since p is a percentage, it must be between 0 and 100. Using this restriction, we can determine a range for C:

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When p is close to 0, e^(-0.05p) becomes close to 1, so C gets very large. Therefore, the cost grows without bound as p takes on positive values near 0.

The Millcreek Watershed Area Was Heavily Strip-Mined for Coal During