A fish population in a lake follows logistic growth: $\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)$. Field data give two points: when $N=2000$ fish the population increases by 300 fish per year, and when $N=8000$ fish the increase is 200 fish per year.

(a) Determine the intrinsic growth rate $r$ (yr⁻¹) and the carrying capacity $K$ (fish).

(b) If a constant harvest of 500 fish per year is introduced, find the equilibrium population(s) and state the long‑term outcome for the fishery.

Question

A fish population in a lake follows logistic growth: $\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)$. Field data give two points: when $N=2000$ fish the population increases by 300 fish per year, and when $N=8000$ fish the increase is 200 fish per year.

(a) Determine the intrinsic growth rate $r$ (yr⁻¹) and the carrying capacity $K$ (fish).

(b) If a constant harvest of 500 fish per year is introduced, find the equilibrium population(s) and state the long‑term outcome for the fishery.

Accepted Answer

No positive equilibrium; the harvest exceeds the maximum sustainable yield, leading to eventual extinction.

Igcse Model Questions Vol1 2021 Biology Question 39

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