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

With the same low-density rate and carrying capacity, the two per-capita growth rates arefor the cubic model andfor logistic growth. The logistic correction is linear in a small population, whereas the cubic correction is quadratic. Consequently the cubic trajectory initially follows pure exponential growth more closely and lies above the logistic trajectory before both approach $K$. Plotting measured per-capita growth against $n$ distinguishes a linear decline from a curve with zero slope at the origin.