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For Students · Logistic Growth

Logistic Growth for a coral colony

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a coral colony live below — adjust the inputs and watch it respond, right in your browser.

Logistic Population GrowthLive

growth with a ceiling

Controls

Presets

Growth rate r

Carrying capacity K

Initial population N₀

Exponential growth assumes unlimited resources and explodes without bound. Logistic growth adds a carrying capacity K: as the population nears K, growth slows and levels off in a characteristic S-curve. It is the foundation of ecology, epidemiology, and resource management.

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Data Inspector

Carrying capacity1000

Max growth atN = 500

Growth rate r0.50

Governing equation

\frac{d P}{d t} = 0.50 P (1 - \frac{P}{1000})

Reading this result: Classic S-curve: from N₀=20 the population grows fastest as it crosses the inflection point N=K/2=500, then decelerates and levels off at the carrying capacity K=1000.

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Frequently asked questions

Is this good for students?: Yes — this version of "Logistic Growth for a coral colony" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.