The cost (in dollars) of removing $p\%$ of the pollutants from the water in a small lake is given by $C = \frac { 23,000 p } { 300 - p } , 0 \leq p

Question

The cost (in dollars) of removing $p\%$ of the pollutants from the water in a small lake is given by $C = \frac { 23,000 p } { 300 - p } , 0 \leq p < 300$ . Evaluate $\lim _ { p \rightarrow 300 ^ { - } } C$ .
A) $\infty$
B) $23,000$
C) $0$
D) $- \infty$
E) $- 23,000$

Quizplus · Accepted Answer

As $p$ approaches 300 from the left, the denominator of the fraction $\frac{23,000p}{300-p}$ approaches 0, making the fraction (and thus the cost $C$) approach infinity.

The Cost (In Dollars) of Removing p%p\%p% Of the Pollutants from the Water in a Small Lake

The Cost (In Dollars) of Removing $p\%$ Of the Pollutants from the Water in a Small Lake