Hurricanes are categorized using the Saffir-Simpson Hurricane Scale, with winds 111–130 miles per hour (mph) corresponding to a category 3 hurricane, winds 131–155 mph corresponding to a category 4 hurricane, and winds in excess of 155 mph corresponding to a category 5 hurricane. The data below represent the number of major hurricanes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2010.

(a) Draw a scatter plot of the data.

(b) Find a sinusoidal function of the form

that models the data.

(c) Draw the sinusoidal function found in part (b) on the scatter plot.

(d) Use a graphing utility to find the sinusoidal function of best fit.

(e) Graph the sinusoidal function of best fit on a scatter plot of the data.

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Decade, x 1921-1930, 1 1931-1940, 2 1941-1950, 3 1951-1960, 4 1961-1970, 5 1971-1980, 6 1981-1990, 7 1991-2000, 8 2001-2010, 9 2011-2020, 10 Major Hurricanes, H 17 16 29 33 27 16 16 27 33 29