The way Professor Waner drives, he burns gas at the rate of $1 - e ^ { - 3 t }$ gallons each hour, t hours after a fill-up. Find the number of gallons of gas he burns in the first 13 hours after a fill-up. Please round the answer to the nearest gallon.
A)16 gallons
B) 11 gallons
C) 14 gallons
D) 17 gallons
E) 13 gallons

Question

The way Professor Waner drives, he burns gas at the rate of $1 - e ^ { - 3 t }$ gallons each hour, t hours after a fill-up. Find the number of gallons of gas he burns in the first 13 hours after a fill-up. Please round the answer to the nearest gallon.  
A)16 gallons
B) 11 gallons
C) 14 gallons
D) 17 gallons
E) 13 gallons

Quizplus · Accepted Answer

To find the total gas burned in the first 13 hours, integrate the rate function $1 - e^{-3t}$ from 0 to 13. The integral is $t + \frac{1}{3}e^{-3t}$ evaluated from 0 to 13, which gives approximately 13 gallons.

The Way Professor Waner Drives, He Burns Gas at the Rate