This interactive simulation allows students to explore two classic mathematical models that describe how populations change over time: the exponential and logistic growth models.
The exponential growth model describes how a population changes if its growth is unlimited. This model can be applied to populations that are small and/or have no competition for resources. The logistic growth model describes how a population changes if there is an upper limit to its growth. This model can be applied to populations that are limited by food, space, competition, and other density-dependent factors.
In this Click & Learn, students can easily graph and explore both the exponential and logistic growth models. Students can set multiple model parameters, such as starting population size, time, and carrying capacity, and observe how population growth is affected by changing any of these variables.
The accompanying worksheets guide students’ exploration. The “Student Worksheet” introduces students to the Click & Learn by having them analyze different components of the models, generate and interpret related plots, and investigate examples of population growth in bacteria and humans. The “African Wildlife Case Studies” handout allows students to apply the Click & Learn to three case studies involving African antelope populations, including wildebeest.
Student Learning Targets
- Describe the assumptions of the exponential and logistic growth models, and how those assumptions do or do not apply to different populations.
- Interpret and apply the exponential and logistic growth equations.
- Explain how the key variables and parameters in these models — such as time, the maximum per capita growth rate, the initial population size, and the carrying capacity — affect population growth.
- Use the exponential and logistic growth models to project and interpret real biological examples.
- Interpret and analyze plots summarizing population growth over time.
carrying capacity, exponential growth, logistic growth, mathematical population model, population density, population growth rate, simulator
The resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International license. No rights are granted to use HHMI’s or BioInteractive’s names or logos independent from this Resource or in any derivative works.
Accessibility Level (WCAG compliance)
HS-LS2-1, HS-LS4-5; SEP2, SEP5
AP Biology (2019)
ENE-4.B, SYI-1.G, SYI-1.H, SYI-3.D; SP2, SP4, SP5, SP6
IB Biology (2016)
AP Environmental Science (2020)
Topic(s): 3.4, 3.5
Learning Objectives & Practices: ERT-3.D, ERT-3.F
IB Environmental Systems and Societies (2017)
Common Core (2010)
ELA.RST.9-12.7, ELA.WHST.9-12.1 Math.A-REI.6, Math.N-Q.1, Math.F-IF.7, Math.S-ID.4, Math.S-ID.7; MP2, MP4
Vision and Change (2009)
CC5; DP2, DP3