A population model developed by the U.S. Census Bureau uses the formula

to estimate the population of the United States (in millions) for every 10th year from the base year 1790. Thus, for instance, t = 0 corresponds to 1790, t = 1 to 1800, t = 10 to 1890, and so on. The model excludes Alaska and Hawaii.

a. Use this formula to compute the population of the contiguous United States for the years 1790, 1800, 1830, 1860, 1880, 1900, 1920, 1940, 1960, 1980, 1990, and 2000.

b. Sketch the graph of P(t). When does this model predict that the population of the contiguous United States will be increasing most rapidly?

P(t) = 202.31 1+ .938-0.314t