As mentioned in Section 17.4.2, the population of the United States in the year 2010 did not seem to be near an asymptote. As an alternative to the logistic growth model, we might entertain the...

As mentioned in Section 17.4.2, the population of the United States in the year 2010 did not seem to be near an asymptote. As an alternative to the logistic growth model, we might entertain the exponential growth model for the period 1790 to 2010; assuming multiplicative errors, this model takes the form

where, as in the text, Y_i
is population, and X_i
= 0; 1; ... ; 21 is time. Because of the multiplicative errors, this model can be transformed to linearity by taking the log of both sides:

where α’ = log_e
α and ε’_i
[ log_e
ε_i. Fit the exponential growth model to the data by linear least-squares regression and graph the fit as in Figure 17.9. [Hint: transform the fitted values back to the original population scale as exp (Y_i
)]. Plot fitted values for the exponential growth model against those for the logistic growth model. Which model appears to do a better job of representing the data?