In 2005, Hurricane Katrina struck the Gulf Coast of the United States, killing 1289 people and causing an estimated $200 billion in damage. The following data represent the number of major hurricane strikes in the United States (category 3, 4, or 5) each decade from 1921 to 2000.

Decade, x ………………………...........…………  Major Hurricanes Striking United States, H

1921–1930, 1 ……………………………………………………………………………………………………… 5

1931–1940, 2 ……………………………………………………………………………………………………… 8

1941–1950, 3 ……………………………………………………………………………………………………… 10

1951–1960, 4 ……………………………………………………………………………………………………… 8

1961–1970, 5 ……………………………………………………………………………………………………… 6

1971–1980, 6 ……………………………………………………………………………………………………… 4

1981–1990, 7 ……………………………………………………………………………………………………… 5

1991–2000, 8 ……………………………………………………………………………………………………… 5

(a) Draw a scatter diagram of the data.Comment on the type of relation that may exist between the two variables.

(b) Use a graphing utility to find the cubic function of best fit that models the relation between decade and number of major hurricanes.

(c) Use the model found in part (b) to predict the number of major hurricanes that struck the United States between 1961 and 1970.

(d) With a graphing utility,draw a scatter diagram of the data and then graph the cubic function of best fit on the scatter diagram.

(e) Concern has risen about the increase in the number and intensity of hurricanes,but some scientists believe this is just a natural fluctuation that could last another decade or two. Use your model to predict the number of major hurricanes that will strike the United States between 2001 and 2010. Does your result appear to agree with what these scientists believe?

(f) From 2001 through 2010, 10 major hurricanes struck the United States. Does this support or contradict your prediction in part (e)?