Question

The daily consumption C (in gallons) of diesel fuel on a farm is modeled by C = 33.7 + 24.7 sin( 353 2t + 10.9) where t is the time (in days), with t= 1 corresponding to January 1. (a) What is the period of the model? days Is it what you expected? Explain

Answer 1

The period of the model can be determined by finding the length of one complete cycle of the sine function.

Step-by-step explanation:

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

The period of the model can be determined by finding the length of one complete cycle of the sine function. In this equation, the coefficient of the variable t inside the sine function determines the period. In this case, the coefficient is 353/2, which means the period of the model is 2π/(353/2) ≈ 0.01777 days.

This period is what we expect because the coefficient of t in the sine function determines how quickly the function oscillates. A larger coefficient means a shorter period, while a smaller coefficient means a longer period.