Calculate population growth using the logistic model with carrying capacity constraints. Model how populations grow exponentially initially, then slow as they approach resource limits.
Population at Time t
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Growth Rate at Time t
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Percentage of Carrying Capacity
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Time to 50% Capacity
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The logistic growth model describes population growth that starts exponentially but slows as the population approaches its carrying capacity. It accounts for resource limitations that prevent unlimited exponential growth.
Carrying capacity (K) is the maximum population size that an environment can sustain indefinitely. It's determined by available resources like food, water, space, and other limiting factors in the ecosystem.
Exponential growth assumes unlimited resources and constant growth rate, while logistic growth accounts for environmental resistance and resource limitations that slow growth as population increases.
In logistic growth, the actual growth rate decreases as population approaches carrying capacity. The formula is: dN/dt = r × N × (1 - N/K), where growth slows as N approaches K.
Examples include bacteria in a petri dish, deer populations in a forest, fish in a lake, or human populations in isolated regions where resources become limiting factors.
A population reaches 50% of carrying capacity at the inflection point of the logistic curve, where growth rate is at its maximum before beginning to decline.
Yes, carrying capacity can change due to environmental factors, climate change, habitat destruction, technological advances, or changes in resource availability.
When population exceeds carrying capacity, it typically leads to resource depletion, increased mortality, decreased birth rates, and eventual population decline back toward sustainable levels.