Chapter 12, Problem 75CP

World population growth The table shows the world population size (in billions) since 1900.

Source: U.S. Bureau of the Census

1. a. Let x denote the number of years since 1900. The exponential regression model fitted to y = population size and x gives $\hat{y}=1.424\times {1.014}^x$. Show that the predicted population sizes are 1.42 billion in 1900 and 6.57 billion in 2010.
2. b. Explain why the fit of the model corresponds to a rate of growth of 1.4% per year.
3. c. For this model fit, explain why the predicted population size (i) doubles after 50 years and (ii) quadruples after 100 years.
4. d. The correlation equals 0.961 between the population size and the year number, and it equals 0.991 between the log of the population size and the year number. What does this suggest about whether the straight-line regression model or the exponential regression model is more appropriate for these data?