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

a. Let x denote the number of years since 1900. The exponential regression model fitted to y = population size and x gives = 1.424 × 1.014x. Show that the predicted population sizes are 1.42 billion in 1900 and 6.57 billion in 2010.
b. Explain why the fit of the model corresponds to a rate of growth rate of 1.4% per year.
c. For this model fit, explain why the predicted population size
(i) Doubles after 50 years and
(ii) Quadruples after 100 years.
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?

Transcribed Image Text:

World Population Sizes (In billons) Year 1900 1910 1920 1930 1940 1950 1960 1970 Populatlon Year Population 1975 1980 1985 1990 1995 2000 2005 2010 1.65 1.75 1.86 2.07 2.30 2.52 3.02 3.69 4.07 4.43 4.83 5.26 5.67 6.07 6.47 6.85