Logistic Growth

Growth that levels off

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Logistic: $\dfrac{dP}{dt} = rP(1 - P/K)$, with carrying capacity $K$.
• Equilibria at $0$ (unstable) and $K$ (stable).
• Fastest growth at $P = K/2$, where the rate is $rK/4$.

Steps

1. Room to grow
2. The S-curve
3. Equilibria
4. A fifth full
5. Halfway there
6. Fastest growth