A Model for Population Growth

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration models population growth over time given the initial population, the growth rate, and the carrying capacity in the biome. The carrying capacity depends on limiting factors that may involve, among other things, the amount of biomass available to the population, predation, and environmental stresses. The model can be represented by the equation , where is the size of the popuation, is time, is the carrying capacity, and is the growth rate. In all cases, a constant, steady state population is eventually reached.

Contributed by: Samer Hassan and Joey Espino (June 2014)
Open content licensed under CC BY-NC-SA



This Demonstration was written in Making Math.

Special thanks to the Netmath Program at the University of Illinois at Urbana/Champaign and the Math Department at Schaumburg High School.


[1] N. Campbell, J. Reece, and L. Urry, Biology AP Edition, 8th ed., San Francisco: Cengage, 2008.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.