Total methods of projection (cont.)

Exponential growth

Instead of assuming that the population is growing by a constant amount, the exponential model assumes that the population is growing at a constant rate. This may be appropriate for expanding communities unaffected by any constraints.

If the population is shrinking over time, its growth rate is negative and one can also fit an exponential model to such data. Constant negative growth is sometimes described as exponential decay.

In order to project the population forward or backward, one requires an estimate its growth rate. Once again, a minimum of two estimates of the population for different dates are needed to calculate this. The model can be fitted to longer time series of estimates of the population by means of a linear regression of the log of population size on time.

In this model:

where r is the constant annual growth rate: