Chapter 4, Problem 70RE

a.

To determine

To graph: The given data and the model in the same viewing window.

Explanation of Solution

Given Information: Given data is $16:59,17:35,18:06,18:38,19:08,19:30,19:28,18:57,18:10,17:21,16:44,16:36$ and model is $S(t)=18.10-1.41\sin \left(\frac{\pi t}{6}+1.55\right)$ .

Graph:

  

b.

To determine

To find: The period of the model and to compare it with expected period.

Answer to Problem 70RE

Period of the model is $12months$ which is the expected period.

Explanation of Solution

Given Information: Given data is $16:59,17:35,18:06,18:38,19:08,19:30,19:28,18:57,18:10,17:21,16:44,16:36$ and model is $S(t)=18.10-1.41\sin \left(\frac{\pi t}{6}+1.55\right)$ .

Calculation and explanation:

Period of the model is $\frac{2\pi }{b}=\frac{2\pi }{\pi /6}=12months$ .

This is the expected period as the sunset times should cycle every year, i.e., $12months$ .

c.

To determine

To find: The amplitude of the model and its significance.

Answer to Problem 70RE

Amplitude of the model is $1.41$, it represents the difference between the earliest sunset time and the latest sunset time.

Explanation of Solution

Given Information: Given data is $16:59,17:35,18:06,18:38,19:08,19:30,19:28,18:57,18:10,17:21,16:44,16:36$ and model is $S(t)=18.10-1.41\sin \left(\frac{\pi t}{6}+1.55\right)$ .

The modulus of the coefficient of sine in $S(t)=18.10-1.41\sin \left(\frac{\pi t}{6}+1.55\right)$ is $1.41$ , which is the amplitude.

It represents the difference between the earliest sunset time and the latest sunset time.