Question: The following data represent the average monthly temperatures for Juneau, Alaska. Month, x .. Average Monthly Temperature, F January, 1 .. 24.2 February, 2 .
The following data represent the average monthly temperatures for Juneau, Alaska.
Month, x …………………………….. Average Monthly Temperature, ˚F
January, 1 …………………………………………………………….. 24.2
February, 2 ……………………………………………………………. 28.4
March, 3 ………………………………………………………………. 32.7
April, 4 ………………………………………………………………… 39.7
May, 5 ………………………………………………………………….. 47.0
June, 6 ………………………………………………………………….. 53.0
July, 7 ………………………………………………………………….. 56.0
August, 8 ………………………………………………………………. 55.0
September, 9 …………………………………………………………… 49.4
October, 10 …………………………………………………………….. 42.2
November, 11 …………………………………………………………… 32.0
December, 12 …………………………………………………………… 27.1
(a) Draw a scatter diagram of the data for one period.
(b) Find a sinusoidal function of the form y = A sin(ωx – ϕ) + B that models the data.
(c) Draw the sinusoidal function found in part (b) on the scatter diagram.
(d) Use a graphing utility to find the sinusoidal function of best fit.
(e) Draw the sinusoidal function of best fit on a scatter diagram of the data.
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