# What is the logistic model of population growth?

Logistic Population Model

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The logistic model of population growth is a mathematical model that describes how a population grows when it is limited by factors such as food, space, or other resources. It is given by the differential equation:

[ \frac{dP}{dt} = rP\left(1 - \frac{P}{K}\right) ]

Where:

- ( \frac{dP}{dt} ) is the rate of change of the population with respect to time ( t ).
- ( P ) is the population size.
- ( r ) is the intrinsic growth rate of the population.
- ( K ) is the carrying capacity of the environment, representing the maximum population size that the environment can support indefinitely.

The logistic model accounts for the fact that as the population grows larger, the growth rate decreases due to limited resources, until the population stabilizes at the carrying capacity ( K ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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