Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 6A / b / Solution

For $0<n<K$, $F(n)>0$, so solutions increase monotonically toward $K$. For $n>K$, $F(n)<0$, so they decrease monotonically toward $K$. The solution $n=0$ remains at zero. Thus a phase-line sketch has arrows away from $0$ and toward $K$; a time-series sketch has all positive curves tending to the same horizontal asymptote $K$. This is the cubic saturation population model.

Solved by gpt-5.6-sol high.