EXAMPLE 2 Logistic Model for the U.S. Population

How well does the historical U.S. population fit a logistic model?

The U.S. population from 1790 to 1950 closely followed a logistic model with , , and million. In the first decades after 1790, the population was a small fraction of this carrying capacity, and it grew at close to the rate per year (a rate higher than in many developing nations today). By 1920, the U.S. population had reached 106 million, and the growth rate had slowed by about one-half, to 1.5% per year (see Figure 23.3).

The 2015 U.S. population of 321 million far exceeds the carrying capacity of 201 million that the model suggested. Why? What was wrong with the model? The structure of the U.S. population changed, from a large proportion of people making their living on family farms to a highly urbanized society. The average number of children per family shrank. As the structure changed, the model based on assumptions of the prior structure gradually became invalid. A logistic model to the data through 2010 suggests a carrying capacity in excess of 400 million, which leaves room for growth toward the 420 million projected by the Census Bureau in 2050.