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The average monthly temperature (°F) in Chicago, Illinois is shown in the table

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25

Month

January

February

March

April

May

June

July

August

September

October

November

December

28

36

48

61

72

74

75

66

55

39

28

a) Plot the average monthly temperature over 2 year period by letting x = 1 correspond to

January of the first year.

b)

Determine a model function of y= A sin (Bx + C) + D Where A, B, C and D are constants.

c) Explain the significance of each constant.

d) Graph the function (y) with the data using Excel. How does well does y model the data?

e) Use the sine regression to find the equation of a sine curve that fit these data.

f)

Determine the maximum and minimum average monthly temperatures and the months

when they occur.

g) Write a short description of some situation that affects our society, country, and/or

world that can be represented using a period function and include the graph of a

periodic graph to support your description.

Fig: 1