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Mathematics

Modeling Population Growth with Logistic Differential Equations

Quick fact

The logistic equation predicts that a population will level off at a 'carrying capacity' determined by the environment, producing an S-shaped growth curve that is far more realistic than unending exponential growth.

Why this is interesting

Imagine a population of rabbits that doubles every month—until the food runs out. What happens then? Why doesn't the population just keep exploding?