EXAMPLE 1 Predicting the U.S. Population

The U.S. population increased at an average effective growth rate of 0.77% per year (including immigration) to 321 million at mid-2015. What would be the anticipated population at mid-2020? What would it be if the effective rate of growth changes to 1% per year, or to 0.5% per year?

We apply the compound interest formula with initial population size (“principal”) 321 million. Using one year as the compounding period and the compound interest formula , where , the projected population size in mid-2020 for a rate is

Because of the limited accuracy of the estimates of population and growth rate, we round off the final answer. The result of a calculation can’t be more precise than the ingredients; we round back to millions because that was the precision of our original data.

Using the same formula, a growth rate of 1% per year leads to a population of 337 million, while a growth rate of 0.5% per year yields 329 million.

So an uncertainty of about one-fourth of one percentage point (0.23–0.27%) in the growth rate has major implications, even over fairly short time horizons. The presence or absence of 3 to 5 million people would have a significant impact on our social and economic systems, in terms of need (or lack thereof) of daycare centers, schools, and products for babies and children. (About one- third of population growth in the United States is projected to come from net immigration.)

At the other end of the age distribution, much of the concern over long-range funding of the Social Security and Medicare programs results from uncertainties over birth and immigration rates. Figure 23.1a gives a graph of the U.S. population in 2015, structured by age and sex, and Figure 23.1b does the same for Nigeria.

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Rates of increase in most developing nations are much higher than in industrialized nations. At a rate of 2.8%, the population of Nigeria, Africa’s most populous country, will grow from 184 million in mid-2015 to 240 million in mid-2025, a shocking increase of one-third—and 60 million people!—in only 10 years. Such projections raise concern over providing sufficient food and resources for all people.

It is not just the number of people that is crucial, but also the population structure. In poorer countries, the proportion of the population over 60 years of age will be 20% by 2050, compared with 8% now; in Japan, where the overall population is expected to decline by one-sixth by then, it will be more than 40%.

Limitations on Growth

A population that keeps adding a fixed percentage each year, like a bank account accumulating compound interest, would eventually grow to astronomical numbers. But no biological population can continue to increase without limit (see Spotlight 23.2). Its growth is eventually constrained by the availability of resources such as food, shelter, and psychological and social “space.” There may be a maximum population size that can be supported by the available resources, the carrying capacity of the environment.

The carrying capacity of an environment is the maximum population size that it can support indefinitely with the available stream of resources.