The table shows the normal daily high temperatures C in Chicago (in degrees Fahrenheit) for month t, with t = 1 corresponding to January.
Months, t ............................................. Chicago, C
1 ......................................................... 31.0
2 ......................................................... 35.3
3 ......................................................... 46.6
4 ......................................................... 59.0
5 ...........................................................70.0
6 ...........................................................79.7
7 ........................................................... 84.1
8 ........................................................... 81.9
9 ........................................................... 74.8
10 ........................................................... 62.3
11 ........................................................... 48.2
12 ........................................................... 34.8
(a) Use a graphing utility to create a scatter plot of the data.
(b) Find a cosine model for the temperatures.
(c) Graph the model and the scatter plot in the same viewing window. How well does the model fit the data?
(d) What is the overall normal daily high temperature?
(e) Use the graphing utility to determine the months during which the normal daily high temperature is above 72°F and below 72°F.