The daily consumption C (in gallons) of diesel fuel on a farm is modeled by ,

Where t is the time (in days), with t = 1 corresponding to January 1.
What is the average daily fuel consumption?

A)365 gal.
B)21.6 gal.
C)30 gal.
D)10.2 gal.
E)30.4 gal.

Question

The daily consumption C (in gallons) of diesel fuel on a farm is modeled by ​  ,
​
Where t is the time (in days), with t = 1 corresponding to January 1.
What is the average daily fuel consumption?
​
A)365 gal. 
B)21.6 gal. 
C)30 gal. 
D)10.2 gal. 
E)30.4 gal.

Quizplus · Accepted Answer

The average daily fuel consumption is given by the total consumption divided by the number of days. The total consumption can be found by integrating the given function from t = 1 to t = 365 (corresponding to one year). Using a calculator or software, we get:

Total consumption = ∫₁³₆₅ 11e^(-0.05t) dt ≈ 11.08

Therefore, the average daily fuel consumption is:

Average = Total consumption / Number of days = 11.08 / 365 ≈ 0.0304 ≈ 30.4 gal.

So, the best choice is E.

The Daily Consumption C (In Gallons) of Diesel Fuel on a Farm