What the Numbers Mean

With the defaults (N₀=100, r=5%, t=10, exponential), the population reaches 165 — +65 individuals (+65%). The same run under the logistic model with K=1,000 gives only about 150, already curving toward the cap as the carrying capacity starts to bite.

The Two Classic Models

Exponential growth N(t) = N₀·e^(rt) describes colonization of empty habitat. Logistic growth N(t) = K/(1+((K−N₀)/N₀)·e^(−rt)) adds the S-curve that real populations show as resources run out — the same math behind sustainable-harvest and conservation decisions.