Let p(t) represent the population of the Las Vegas metropolitan area t years after 1950, as shown in the table and figure.

a. Compute the average rate of growth of Las Vegas from 1970 to 1980.

b. Explain why the average rate of growth calculated in part (a) is a good estimate of the instantaneous rate of growth of Las Vegas in 1975.

c. Compute the average rate of growth of Las Vegas from 1990 to 2000. Is the average rate of growth an overestimate or underestimate of the instantaneous rate of growth of Las Vegas in 2000? Approximate the growth rate in 2000.

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1950 Year 1960 1970 1980 1990 2000 2010 40 10 20 30 50 60 59,900 139,126 304,744 528,000 852,737 1,563,282 1,951,269 p(t) (Source: U.S. Bureau of Census) PA 2000 1600 1200 800 400 t 10 20 30 40 50 60 Years after 1950 Population (thousands)