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, which in this case is $\frac{2\pi}{365}$. The period of a sine function is given by $\frac{2\pi}{\text{coefficient of } t}$, which in this case results in a period of 365 days, indicating that the model completes one full cycle every 365 days.

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