Logistic Growth

A model for a quantity that increases quickly at first and then more slowly as the quantity approaches an upper limit. This model is used for such phenomena as the increasing use of a new technology, spread of a disease, or saturation of a market (sales).

The equation for the logistic model is . Here, t is time, N stands for the amount at time t, N₀ is the initial amount (at time 0), K is the maximum amount that can be sustained, and r is the rate of growth when N is very small compared to K.

Note: The logistic growth model can be obtained by solving the differential equation