The average number of vehicles waiting in line at a toll booth of a super highway is modeled by the function $\mathrm { n } ( \mathrm { x } ) = \frac { \mathrm { x } ^ { 2 } } { 0.5 ( 1 - \mathrm { x } ) }$ , where x is a quantity between 0 and 1 known as the traffic intensity. To the nearest tenth, find the average number of vehicles waiting if the traffic intensity is .81.
A) 1.6 vehicles
B) 3.5 vehicles
C) 6.9 vehicles
D) 8.5 vehicles

Question

Quizplus · Accepted Answer

To find the average number of vehicles waiting, substitute $x = 0.81$ into the given function: $n(x) = \frac{x^2}{0.5(1-x)}$. This gives $n(0.81) = \frac{0.81^2}{0.5(1-0.81)} = \frac{0.6561}{0.5(0.19)} = \frac{0.6561}{0.095} = 6.906$, which rounds to 6.9 vehicles.

The Average Number of Vehicles Waiting in Line at a Toll