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Chapter 3: Problem 5

A logistic growth model has the form ________.

Short Answer

Expert verified
A logistic growth model has the form: \(\frac{dP}{dt} = rP(1-\frac{P}{K})\).

Step by step solution

01

Define the Logistic Growth Model

A logistic growth model describes a phenomenon that increases gradually at first, more rapidly in the middle growth period, and slowly at the end, approaching a maximum of carrying capacity. It is encapsulated in the logistical function.
02

Formulate the Logistic Function

The logistic function is usually given by the following differential equation: \(\frac{dP}{dt} = rP(1-\frac{P}{K})\), where: \(P(t)\) is the size of the population at time \(t\), \(r\) is the rate of maximum population growth, \(K\) is the carrying capacity of the population, \(\frac{dP}{dt}\) is the rate of change of the population at time \(t\).

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