The daily consumption C (in gallons) of diesel fuel on a farm is modeled by $C = 30.8 + 21.6 \sin \left( \frac { 2 \pi t } { 365 } + 10.9 \right)$ ,

Where t is the time (in days), with t = 1 corresponding to January 1.
What is the period of the model?

A)31 days
B)22 days
C)183 days
D)365 days
E)30 days

Question

The daily consumption C (in gallons) of diesel fuel on a farm is modeled by   $C = 30.8 + 21.6 \sin \left( \frac { 2 \pi t } { 365 } + 10.9 \right)$ ,
 
Where t is the time (in days), with t = 1 corresponding to January 1.
What is the period of the model?
 
A)31 days
B)22 days
C)183 days
D)365 days
E)30 days

Quizplus · Accepted Answer

The period of the sine function is determined by the coefficient of $t$ inside the sine function. The general form for the period of a sine function is $P = \frac{2\pi}{|b|}$, where $b$ is the coefficient of $t$. In this model, $b = \frac{2\pi}{365}$, so the period $P = \frac{2\pi}{\frac{2\pi}{365}} = 365$ days. This means the model completes one full cycle every 365 days, corresponding to one year.

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