EXAMPLE 3 Use sinusoidal regression Energy The table below shows the number of kilowatt hours K (in thousands) used each month for a given year by a hangar.

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EXAMPLE 3 Use sinusoidal regression Energy The table below shows the number of kilowatt hours K (in thousands) used each month for a given year by a hangar at the Cape Canaveral Air Station in Florida. The time t is measured in months, with t = 1 representing January. Write a trigonometric model that gives K as a function of t.

EXAMPLE 3 Use sinusoidal regression SOLUTION STEP 1 Enter the data in a graphing calculator. STEP 2 Make a scatter plot.

EXAMPLE 3 Use sinusoidal regression STEP 3 Perform a sinusoidal regression, because the scatter plot appears sinusoidal. STEP 4 Graph the model and the data in the same viewing window.

EXAMPLE 3 Use sinusoidal regression ANSWER The model appears to be a good fit. So, a model for the data is K = 23.9 sin (0.533t – 2.69)

GUIDED PRACTICE for Example 3 4. METEOROLOGY Use a graphing calculator to write a sine model that gives the average daily temperature T (in degrees Fahrenheit) for Boston, Massachusetts, as a function of the time t (in months), where t = 1 represents January. ANSWER T = 21.8 sin (0.514t – 2.18)