Exponential growth and decay can be determined with the following equation: N = (NI)(e^kt). In this equation, "N" refers to the final population, "NI" is the starting population, "t" is the time over which the growth or decay took place and the "k" represents the growth or decay constant. If necessary, this equation may be rearranged to find any of these variables.
- Determine if there is population growth or decay
Determine if this is a growth or decay problem by observing the value of the "k." If this value is positive, then the population is growing. If the value is negative, then there is population decay.
- Determine the number of time periods
Determine the number of time periods to find the value of "t." This value should be in the same units as the rate of growth and may require some basic math. For instance, if the rate is per month and the time elapsed is three years, the value for "t" will be 36.
- Perform the calculations
Calculate the value for the final population using the aforementioned equation. To ensure that your calculations are accurate, you may want to multiply "k" by "t" before taking them to the exponential power (e).