Logistic Models

Models of the form a+blnx, logarithmic scales and linearizing exponential data.

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Logistic Models

AHL AI 2.9

A logistic model describes growth that appears exponential for smaller values but slows as it approaches a carrying capacity, represented by a horizontal asymptote above the curve.

Logistic models are given by the general equation f(x)=1+Ce−kxL, where L is the carrying capacity. Logistic models are particularly effective for modelling population growth, as they tend to grow exponentially from small numbers yet have a carrying capacity capped by the scarcity of space, food, and water. k is often called the intrinsic rate, and it represents the rate of growth of a quantity before it nears carrying capacity. Finally, C controls the initial population since f(0)=1+CL, where f(0) is the initial population.

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Logistic Models

AHL AI 2.9

A logistic model describes growth that appears exponential for smaller values but slows as it approaches a carrying capacity, represented by a horizontal asymptote above the curve.

Logistic models are given by the general equation f(x)=1+Ce−kxL, where L is the carrying capacity. Logistic models are particularly effective for modelling population growth, as they tend to grow exponentially from small numbers yet have a carrying capacity capped by the scarcity of space, food, and water. k is often called the intrinsic rate, and it represents the rate of growth of a quantity before it nears carrying capacity. Finally, C controls the initial population since f(0)=1+CL, where f(0) is the initial population.

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