Algebra
Time to reach a target population
Inverts the curve, so you can ask when a milestone will be reached.
The Formula
t = ln( ((K - P0) / P0) / (K/P - 1) ) / r
Inverts the curve, so you can ask when a milestone will be reached.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| t | Time | unit of time | How long until the target is reached. |
| P | Target population | units of population | The level you want to know the date of. |
| K | Carrying capacity | units of population | The ceiling of the model. |
What Each Symbol Means
tunit of time
Time
How long until the target is reached.
Punits of population
Target population
The level you want to know the date of.
Kunits of population
Carrying capacity
The ceiling of the model.
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.