Exponential Population Growth

This formula predicts how a population changes when each individual adds to the total at a constant proportional rate, so the increase in one time interval depends on how many organisms are already present. The constant e appears because continuous growth can be built up from many tiny compounding steps, rather than from fixed jumps. In environmental science, it gives a good approximation when resources are plentiful and limiting factors like crowding or predation are negligible over the time period considered.

Use this model for short-term growth of bacteria, algae, insects, or invasive species when the per-capita growth rate is roughly constant. It is also useful as a starting point for estimating future population size before adding real-world limits such as carrying capacity.

• Using r as a percent without converting it to a decimal
• Putting the time into the exponent with the wrong unit, such as hours when r is per day
• Applying the model when the population is clearly limited by food, space, or other constraints