The daily consumption C (in gallons) of diesel fuel on a farm is modeled by
$C = 30.4 + 21.6 \sin \left( \frac { 2 \pi t } { 365 } + 10.2 \right)$ ,

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 
 $C = 30.4 + 21.6 \sin \left( \frac { 2 \pi t } { 365 } + 10.2 \right)$ ,
 
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 constant term in the model, which is 30.4 gallons. The sine function oscillates around 0, so its average contribution over time is 0, leaving only the constant term to define the average.

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