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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-1/6e/a/i/solution

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Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 6E / a / i / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

The per-capita net growth rate is the birth rate minus the death rate,

b e^{- a N} - d .

Multiplying by the population size gives the ordinary differential equation

\frac{d N}{d t} = N (b e^{- a N} - d) .

This is the exponential density-dependent birth model.

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