The growth of a population can be calculated in one of two ways. If both the initial date and later date, between which the amount of growth is being calculated, are known, the growth is equal to the difference when the former is subtracted from the latter. Calculating the projected growth of a population is more complicated. In this scenario, the initial population size must be known, and the final population is determined using the exponential formula N(t) = N(0)e^(rt), where N(t) is the population size at a given time, N(0) is the initial population size, e is the base of natural logarithms with a constant value of 2.72, r is the growth rate, and t is time.

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## Instructions

- 1
Determine the population size of the community in question at the earliest time from which growth is to be calculated through public record or firsthand research. Denote this information as N(0).

- 2
Determine the population size of the community at a time that is later than the initial point in time (0) and earlier than the final point in time. For example, if you are calculating the population size of a village between 1931 and the present, you might choose to find the population of the village in 1940 for the purpose of this step.

- 3
Subtract the initial population size from the population size at a date between the initial date and the date at which the growth is being determined.

- 4
Divide the difference between the initial population size and the sample population size by the initial population size. The result is the population's growth rate (r).

Written out, this equation appears as follows:

r = (N(t) -- N(0)) / N(0), where N(t) is a sample population size after the initial population size and the time of inquiry.

- 5
Multiply the initial population size by e (2.72) to the power of rate and time multiplied.

Written out, this equation appears as follows: N(t) = N(0)e^(rt).

This equation yields the projected population size at the time in question.

- 6
Subtract the initial population size N(0) from the final population size N(t). The difference is equal to the growth of the population between N(0) and N(t).