Exponential Population Growth

This equation models a population that increases by a constant proportion per unit time, so the bigger the population gets, the faster it grows in absolute terms. The factor e^{rt} comes from continuous growth: instead of adding a fixed number each step, each individual contributes to growth all the time, which leads to an exponential curve. It is a good approximation when resources are effectively unlimited and birth/death rates stay constant over the time period considered.

Use this formula for idealized population growth problems in biology, such as bacteria in a fresh nutrient medium, cells in early culture, or any organism growing with very low competition and no resource limits. It is also useful as a baseline model before introducing more realistic limits like carrying capacity.

• Using t in the wrong units for the growth rate, such as plugging in days when r is per hour
• Treating r as a percentage without converting it to a decimal, for example using 12 instead of 0.12
• Confusing exponential growth with linear growth and adding the same number each time instead of multiplying by e^{rt}