12.57 U.S. population growth The table shows the approximate U.S. population size (in millions) at 10-year intervals beginning in 1900. Let x denote the number of decades since 1900. That is, 1900 is x = 0, 1910 is x = 1, and so forth. The exponential regression model fitted to y = population size and x gives yn = 81.14 * 1.1339x.

a. Show that the predicted population sizes are 81.14 million in 1900 and 323.3 million in 2010.

b. Explain how to interpret the value 1.1339 in the prediction equation.

c. The correlation equals 0.98 between the log of the population size and the year number. What does this suggest about whether the exponential regression model is appropriate for these data?

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Population U.S. population sizes (in millions) from 1900 to 2010 Population Population Year Size Year Size Year Size 1900 76.2 1940 132.1 1980 226.5 1910 92.2 1950 150.7 1990 248.7 1920 106.0 1960 179.3 2000 281.4 1930 122.8 1970 203.3 2010 308.7