The monthly residential consumption of natural gas in Pennsylvania for 2009 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

that models this 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 total natural gas consumption for the year for residential customers in Pennsylvania and compare it to the actual value.

d. Calculate the period of the function found in part b. Is this period reasonable?

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Month January February March April May June July August September October November December Consumption (million cubic feet) 47,599 40,659 30,877 19,169 8726 5317 4576 4084 4711 11,175 16,944 33,740