The population of the United States (in millions) by decade is given in the table, where t is the number of years after 1900. These data are plotted and fitted with a smooth curve y = p(t) in the figure.

a. Compute the average rate of population growth from 1950 to 1960.

b. Explain why the average rate of growth from 1950 to 1960 is a good approximation to the (instantaneous) rate of growth in 1955.

c. Estimate the instantaneous rate of growth in 1985.

Transcribed Image Text:

Year 1900 1910 1920 1930 1940 1950 10 20 30 40 50 p(t) 106.02 132.16 76.21 92.23 123.2 152.32 1990 Year 1960 1970 1980 2000 2010 90 100 60 70 80 110 308.94 p(t) 179.32 203.30 226.54 248.71 281.42 Ул 320 240 160 y = p(t) 80 20 40 60 80 100 Years after 1900 U.S. population (millions)