The average number of vehicles waiting in line at a toll booth of a super highway is modeled by the function $n(x)=\frac{x^{2}}{0.5(1-x)}$, where $x$ is a quantity between 0 and 1 known as the traffic intensity.
What happens to the average number of vehicles waiting as traffic intensity increases?
A) The average number of vehicles waiting increases.
B) The average number of vehicles waiting decreases at first, but then increases.
C) The average number of vehicles waiting decreases.
D) The average number of vehicles waiting remains constant.

Question

Quizplus · Accepted Answer

As traffic intensity $x$ approaches 1, the denominator of the function $n(x)=\frac{x^{2}}{0.5(1-x)}$ approaches 0, causing the value of $n(x)$ to increase towards infinity. This means the average number of vehicles waiting increases as traffic intensity increases.

The Average Number of Vehicles Waiting in Line at a Toll