The amount of electricity (in trillion BTUs) consumed by U.S. residential customers in 2009 is given 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 electrical consumption is periodic?

b. Use a calculator with trigonometric regression to find a trigonometric function of the form

that models this data when t is the month and C(t) is the amount of electricity consumed (in trillion BTUs). Graph the function on the same calculator window as the data.

c. Determine the period, T, of the function found in part b. Discuss the reasonableness of this period.

d. Use the function from part b to estimate the consumption for the month of September, and compare it to the actual value.

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Month January February March April May June July August September October November December Electricity (trillion BTUs) 464 394 362 312 321 390 469 472 393 336 316 421