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Continuous Growth Models

This worksheet compares user-input growth data with predictions under linear, exponential, and logistic models of growth. Students can input parameters for each model; the program graphs the results and computes a crude goodness-of-fit measure. Introduces concepts of modeling and statistical analysis that can be more thoroughly explored using standard statistics software (JMP, SAS, etc.)

Source

Author(s):
Tony Weisstein, Truman State University

Published by: BioQUEST Curriculum Consortium

OS: all

User Manuals and Curricular Materials
Download
Popular Text Citations

Baker, G. L.; Gollub, J. P. 1990. ‘The logistic map’ in: Chaotic Dynamics: an introduction. NY: Cambridge University Press.

Research Articles

Zwanzig, R. 1973. Generalized Verhulst Laws for Population Growth. Proc Natl Acad Sci U S A. 70:3048–3051.

Urszula Fory’s, A. M. 2003. Logistic equations in tumor growth modeling. Int. J. Appl. Math. Comput. Sci 13:317-325.

Betty Tang and Gail S.K. Wolkowicz, (1992) "Mathematical Models of Microbial Growth and Competition in the Chemostat Regulated by Cell-Bound Extracellular Enzymes," Journal of Mathematical Biology 31, 1-23.

Julien Arino, Lin Wang, and Gail S. K. Wolkowicz, ``An alternative formulation for a delayed logistic equation,'' to appear in Journal of Theoretical Biology.

Education Research & Pedagogical Materials

Directions for simulating Verhulst equations on a TI-83 calculator

Steve Baedke, X-next logistic model, James Madison University, Department of Geology and Environmental Sciences

Data Sources

United Nations. World Population Prospects: The 2004 Revision Population Database

Tutorial & Background materials

T.J. Nelson, Population Dynamics

Nardin Patrizia , The Verhulst Equation

Citation
Weisstein Tony () Continuous Growth Models. A module of the Biological ESTEEM Collection, published by the BioQUEST Curriculum Consortium. URL: http://bioquest.org/esteem/esteem_details.php?product_id=197