The monthly residential consumption of natural gas in Pennsylvania for 2019 is found in the following table.

(a) Plot the data, letting t = 1 correspond to January, t = 2 to February, and so on. Is it reasonable to assume that the monthly consumption of energy is periodic?
(b) Find the trigonometric function of the form C(t) = a sin(bt + c) + d that models these data when t is the month of the year and C(t) is the natural gas consumption. Graph the function on the same calculator window as the data.
(c) Estimate the rate at which the consumption is changing in November.
(d) Estimate the total natural gas consumption for the year for residential customers in Pennsylvania and compare it to the actual value.
(e) Calculate the period of the function found in part (b). What would you expect the period to be? Discuss possible reasons for any discrepancy.

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Month January February March April May June July August September October November December Consumption (million cubic feet) 50,766 40,517 35,708 14,539 8511 4891 4043 3960 4233 8029 23,915 39,279