A population of algae in a tank grows logistically from 20 cells, with r = 0.4 per hour and a…

Logistic growth: $\dfrac{dN}{dt} = rN\left(1 - \dfrac{N}{K}\right)$. An Euler step: N = N + r * N * (1 - N / K) * dt. Exact curve: $N = \dfrac{K}{1 + (K/N_0 - 1)e^{-rt}}$. It reaches $\dfrac{K}{2}$ at $t = \dfrac{\ln(K/N_0 - 1)}{r}$, where it grows fastest, at $\dfrac{rK}{4}$.