Calculus › Section G · Differential equations › Topic G.4
The logistic equation and population models
Exponential growth is a runaway train: it never slows down. Real populations hit limits set by food, space and rivals. The logistic equation adds that brake, and together with predator-prey and epidemic models it forms the basic toolkit for modelling living populations.
In this topic
- Why exponential growth cannot last
- The logistic equation
- Equilibria: where growth stops
- Where growth is fastest
- Worked example: solving the logistic equation
- Worked example: a stocked lake
- Harvesting and sustainable yield
- Two species: the predator-prey model
- Why predator and prey cycle
- Epidemics: the SIR model
- Common mistakes to avoid
- Key takeaways
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Standards: 7 (BC)