Algebra
The logistic growth function
The closed form solution, giving the population directly at any time.
The Formula
P(t) = K / (1 + ((K - P0) / P0) x e^(-rt))
The closed form solution, giving the population directly at any time.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| P(t) | Population at time t | units of population | The size after t units of time. |
| K | Carrying capacity | units of population | The ceiling the population approaches. |
| P0 | Starting population | units of population | The size at time zero. |
| r | Growth rate | per unit time | The intrinsic rate per unit of time. |
What Each Symbol Means
P(t)units of population
Population at time t
The size after t units of time.
Kunits of population
Carrying capacity
The ceiling the population approaches.
P0units of population
Starting population
The size at time zero.
rper unit time
Growth rate
The intrinsic rate per unit of time.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate logistic growth page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Logistic Growth, filed under Math. Every number the guide produces comes from substituting into this one line.