Chapter 1.5, Problem 86E

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

$C=30.3+21.6\text{sin}\left(\frac{2\pi t}{365}+10.9\right)$

where $t$ is the time (in days), with $t=1$ corresponding to January $1$.

(a) What is the period of the model? Is it what you expected? Explain.

(b) What is the average daily fuel consumption? Which value in the model did you use? Explain.

(c) Use a graphing utility to graph the model. Use the graph to approximate the time of the year when consumption exceeds 40 gallons per day.