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 $2,860.
B)Near p = 0, the cost grows without bound.
C)Near p = 0, the cost approaches $286,000.
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 $2,860. 
B)Near p = 0, the cost grows without bound. 
C)Near p = 0, the cost approaches $286,000. 
D)Near p = 0, cost approaches $0. 
E)Near p = 0, the cost becomes negative.

Quizplus · Accepted Answer

The range of p is restricted to be between 0 and 100 (inclusive) since p is a percentage. To obtain an accurate graph, we need to avoid negative values or division by zero, which means p cannot be close to 0. When p is very small, the exponential term in the denominator becomes very large, causing the denominator to approach 0 and the fraction to approach infinity. Therefore, the cost grows without bound as p approaches 0. Choice B is the best choice as it accurately describes the behavior of the cost near p = 0.

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