Human Population Dynamics

The exam's most-missed calculations live in this topic: the rate of natural increase, the rule of 70, and the year a population doubles. Each is short, but each has a trap. This page builds them step by step, with every setup shown the way a reader wants to see it.

Crude birth and death rates

The crude birth rate (CBR) is the number of births in a year for every 1,000 people. The crude death rate (CDR) is the number of deaths in a year for every 1,000 people. "Crude" means they count the whole population, not one age group.

To get a crude rate from counts, divide by the population and multiply by 1,000. A country of 50 million people (50 million $= 5 \times 10^{7} = 50{,}000{,}000$) with 1,100,000 births has

$$\text{CBR} = \frac{1{,}100{,}000}{50{,}000{,}000} \times 1{,}000 = 22 \text{ births per 1,000 people}$$

Rate of natural increase

The rate of natural increase is growth from births and deaths alone, as a percent per year:

$$\text{rate of natural increase } (\%) = \frac{\text{CBR} - \text{CDR}}{10}$$

Why divide by 10? The rates are per 1,000 people, and a percent is per 100. Dividing by 10 turns "per 1,000" into "per 100".

The rule of 70 and the year a population doubles

For a population growing at a steady percent each year, the doubling time is about $\frac{70}{\text{growth rate in }\%}$ years. Use the rate in percent (2.8, not 0.028).

To go from 12 million to 48 million is two doublings (12 to 24 to 48). At 3.5% a year the doubling time is $\frac{70}{3.5} = 20$ years, so it takes $2 \times 20 = 40$ years.

Migration

Births and deaths are only part of the story. Immigration (people moving in) adds to a population, and emigration (people moving out) subtracts. The total growth rate counts all four:

$$\text{growth rate } (\%) = \frac{(\text{births} + \text{immigrants}) - (\text{deaths} + \text{emigrants})}{\text{population}} \times 100$$

A country whose deaths outnumber its births can still grow if enough people move in.

Malthus and the limits to growth

In 1798 Thomas Malthus argued that population grows in a doubling series while food grows only by steady additions, so famine, disease or war would hold population back. Since then the world has grown from about 1 billion people (around 1800) to 8 billion (2022, United Nations), and food per person has risen in most places. Many scientists still ask Malthus's question about limits, pointing to soil, fresh water and fuel that are being used faster than they are replaced.

On the exam