No population grows forever. See how a carrying capacity bends runaway exponential growth into the S-shaped curve that describes real populations.
Logistic Population GrowthLive
growth with a ceiling
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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.
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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How it works
Exponential growth assumes unlimited resources; logistic growth adds a carrying capacity K where the population levels off. Growth is fastest at K/2 and slows to zero as the population approaches its limit. This single equation underlies ecology, the spread of innovations, and early epidemic growth.
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