How logistic growth behaves

Logistic growth starts like exponential growth, but it slows as the population approaches the carrying capacity KK.

That flattening matters when resources are limited. The curve helps you see both the fast-growth phase and the gradual leveling near capacity.

The half-capacity time is a useful milestone because it marks the middle of the S-shaped transition.

Input tips

  • Keep the initial value P0P_0 below the carrying capacity KK.
  • Use smaller time steps when you want a denser table and smoother visual checkpoints.
  • The model assumes positive growth rate rr and a fixed carrying capacity.