?Suppose the rate of gasoline consumption in the United States can be modeled by a

Chapter 5, Problem 199

(choose chapter or problem)

Suppose the rate of gasoline consumption in the United States can be modeled by a sinusoidal function of the form \(\left(11.21-\cos \left(\frac{\pi t}{6}\right)\right) \times 10^{9} \mathrm{gal} / \mathrm{mo}\).

(a) What is the average monthly consumption, and for which values of t is the rate at time t equal to the average rate?

(b) What is the number of gallons of gasoline consumed in the United States in a year?

(c) Write an integral that expresses the average monthly U.S. gas consumption during the part of the year between the beginning of April (t=3) and the end of September (t=9).

Text Transcription:

(11.21-cos (pi t/6)) times 10^9 gal/mo