# Population growth rate - Logistic equation

## Description

In biology or human geography, population growth is the increase in the number of individuals in a population.

The “population growth rate” is the rate at which the number of individuals in a population increases in a given time period, expressed as a fraction of the initial population. Specifically, population growth rate refers to the change in population over a unit time period, often expressed as a percentage of the number of individuals in the population at the beginning of that period. This can be written as the shown formula, valid for a sufficiently small time interval.

Most populations do not grow exponentially, rather they follow a logistic model. Once the population has reached its carrying capacity, it will stabilize and the exponential curve will level off towards the carrying capacity, which is usually when a population has depleted most its natural resources.

As the logistic equation is a separable differential equation, the population may be solved explicitly by the shown formula

Related formulas## Variables

P(t) | The population after time t (people) |

K | the carrying capacity of the population (people) |

P_{0} | the initial population at time 0 (people) |

r | relative growth rate coefficient (dimensionless) |

t | time of the estimation (year) (dimensionless) |