Chapter 4.5, Problem 86E

(a)

To determine

To find: the period of the model.

Answer to Problem 86E

Period of the model is 365 days.

Same answer is expected as because there are 365 days in a year.

Explanation of Solution

Given information:

The daily consumption $C$ of diesel fuel on a farm is modeled by

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

Where $t$ is the time, with $t=1$ corresponding to January 1.

Calculation:

The period of the model is,

  $\begin{array}{c}p=\frac{2\pi }{\left(\frac{2\pi }{365}\right)}\\ =\frac{2\pi \left(365\right)}{2\pi }\\ =365\end{array}$

Yes, we expected the same answer as because there are 365 days in a year.

(b)

To determine

To find: the average daily fuel consumption, to find the model did use.

Answer to Problem 86E

30.3 gal

Explanation of Solution

Calculation:

The average daily fuel consumption is 30.3 gal

We used the constant term for it.

(c)

To determine

To find: a graph of the model, and to approximate the time of the year when consumption exceeds 40 gallons per day.

Answer to Problem 86E

The time of the year when the fuel consumption exceeds 40 gals per day is

  $124<t<252$ .

Explanation of Solution

Let us plot the graph for the given model,

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

  

Hence, the time of the year when the fuel consumption exceeds 40 gals per day is

  $124<t<252$ .