Growth
Introduction
We have seen that the NRR is a measure of population growth because an NRR of more than one means that each woman will bear on average more than one daughter and therefore the size of the daughter’s generation will be larger than the mother’s, if fertility and mortality rates are unchanged. The ratio NRR:1 is the amount that the population grows or shrinks in a generation.
However, the NRR tells us nothing about how quickly the population is growing or shrinking because we do not know how long it takes for each generation to replace itself.
In order to calculate an annual growth rate based on the NRR, it is necessary to know the average generation length. There are various ways to estimate this measure.
It is also important to understand that population growth in human populations can be expressed using an exponential function (see box and session 6, page 12 
).
Exponential growth
Exponential functions are used to describe natural processes of growth and decay in which the rate of change over time (increase or decrease) is constant and the absolute change per unit time is proportional to the size of the growing or decaying entity.
For example, imagine some bacteria in a petri dish. If conditions are stable, their rate of growth will increase in proportion to the population size, because there will be increasingly more bacteria present to reproduce. The same is true for human populations. Exponential growth expresses continuous increase or decrease, and is appropriate for measuring change in living populations because births and deaths are happening all the time.
You may also be familiar with the concept of exponential growth from finance. If your bank account accumulates interest continuously throughout the year, rather than in one annual increment, this is a form of exponential growth.
If the initial population size is defined as P0, and growth is accumulating exponentially over time, then the population size after time t will be:
Pt = P0 . ert
The number e, like the number π, is an infinite decimal, to the first five places of decimals e = 2.71828.