Chapter 1.4, Problem 99E

(a)

To determine

To calculate: The model of the form, $y=a\sin \left(bt+c\right)+d$ for each city from the below table which shows the average high temperature (in degrees Fahrenheit) in Boston, Massachusetts $\left(B\right)$,and Fairbanks, Alaska $\left(F\right)$ using the regression feature of a graphing utility.

$\begin{array}{ccc}\text{Month}& \begin{array}{c}\text{Boston,}\\ B\end{array}& \begin{array}{l}\text{Fairbanks,}\\ F\end{array}\\ \text{January}& 33& 1\\ \text{March}& 41& 31\\ \text{June}& 72& 71\\ \text{August}& 83& 62\\ \text{November}& 56& 17\end{array}$

(b)

To determine

To calculate: The monthly average high temperatures (in degrees Fahrenheit) for two cities in February, April, May, July, September, October, and December by using the model from part (a).

(c)

To determine

To graph: The both models of Boston and Fairbanks in the same viewing window by using the graphing utility and compare the temperatures for the two cities.