## Math in the Natural Sciences## Math and the Environment |

## What is a logistic equation? |

A logistic equation (resulting in a curve on a graph) represents the exponential increase in numbers of a species until it reaches the carrying capacity in its specific environment. This carrying capacity, usually referred to by the letter *K,* is the maximum population size that can be regularly sustained by an environment. Change the environment and *K* changes, for example, by such events as adding a predator, removing a competitor, or adding a parasite. The notation that follows (in the form of a differential equation) represents a rate of population increase that is limited by interspecific competition (see above):

in which *N* is the population size, *t* is time, *K* is the carrying capacity, and *r* is the intrinsic rate of increase.