Chapter 9, Problem 32CR

To determine

To write the model that gives $P$ as a function of $t$ and interpret the period of its graph and to interpret its period.

Answer to Problem 32CR

  $P(t)=1.0764\sin (0.585t+3.954)+1.528$

Explanation of Solution

Given:

The given data is

  

Calculation:

First let us plot the scatter plot of the given data as follows-

  

  $y=1.0764\sin (0.585t+3.954)+1.528$

After having a close look on the curve it seems that the curve is sinusoidal, so let us perform the sinusoidal regression on it.

  

So, the model of the curve is as follows-

  $P(t)=1.0764\sin (0.585t+3.954)+1.528$

The period the graph is $\frac{2\pi }{0.585}\approx 12$ . And a year has months so, the pattern is expected to repeat itself.