Solve the problem.
-The rate of water usage for a business, in gallons per hour, is given by $W ( t ) = 25$ te ${ } ^ { - t }$, where $t$ is the number of hours since midnight. Find the average rate of water usage over the interval $0 \leq \mathrm { t } \leq 6$.
A) 0.07 gallons per hour
B) 4.09 gallons per hour
C) 4.12 gallons per hour
D) 4.24 gallons per hour

Question

Quizplus · Accepted Answer

The average rate of water usage over the interval $0 \leq t \leq 6$ can be found by integrating the rate function $W(t) = 25te^{-t}$ from $t = 0$ to $t = 6$ and then dividing by the length of the interval, which is 6 hours. The integral of $25te^{-t}$ from 0 to 6 is $\int_{0}^{6} 25te^{-t} dt$. This evaluates to $-25(te^{-t} + e^{-t})\Big|_{0}^{6}$. Evaluating this expression from 0 to 6 gives a result, and when divided by 6, it gives the average rate of water usage over the specified interval. The correct answer, after performing these calculations, is approximately 4.09 gallons per hour.

Solve the Problem W(t)=25W ( t ) = 25W(t)=25 Te −t{ } ^ { - t }−t

Solve the Problem $W ( t ) = 25$ Te ${ } ^ { - t }$