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Logistic Equation

The logistic equation is used to calculate population growth—the increase in the number of individuals in a population.

The population equals the product of the maximum sustainable population and the initial population divided by the sum of the initial population and the product of the difference between the maximum sustainable population and the initial population and the exponetial of the negative of the rate of maximum population growth times time.

Formula

QuantityVariable["N", "Unitless"] == (QuantityVariable["K", "Unitless"]*QuantityVariable[Subscript["N", "0"], "Unitless"])/((QuantityVariable["K", "Unitless"] - QuantityVariable[Subscript["N", "0"], "Unitless"])/E^(QuantityVariable["r", "GrowthConstant"]*QuantityVariable["t", "Time"]) + QuantityVariable[Subscript["N", "0"], "Unitless"])

Forms

Examples

Get the resource:

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ResourceObject["Logistic Equation"]
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Get the formula:

In[2]:=
FormulaData[ResourceObject["Logistic Equation"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Logistic Equation"], {QuantityVariable["t","Time"] -> Quantity[5, "Years"], QuantityVariable["K","Unitless"] -> 10000, QuantityVariable["r","GrowthConstant"] -> Quantity[1, 1/("Years")], QuantityVariable["N","Unitless"] -> 5000}]
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