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.)

• Documentation

Logistic Function

Belgian mathematician who introduced the Verhulst equation (also known as the logistic equation ) to model human population growth in 1838. He quit his literary studies to devote himself to mathematics. As an undergraduate at the University of Ghent, he was awarded two academic prizes for his works on the calculus of variations. Later, he published papers on number theory and physics.

Verhulst, P. F., (1838). Notice sur la loi que la population pursuit dans son accroissement. Corresp. Math. Phys. 10:113-121.

Verhulst, P. F. 1845. Recherches Mathematiques sur La Loi D'Accroissement de la Population, Nouveaux Memoires de l'Academie Royale des Sciences et Belles-Lettres de Bruxelles, 18, Art. 1, 1-45. (Mathematical Researches into the Law of Population Growth Increase)

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

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.

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

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

T.J. Nelson, Population Dynamics

Nardin Patrizia , The Verhulst Equation