The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape. The assignment contains two opposite, but related tasks: solving a differential equation and constructing a differential equation for a given function as its solution.
The Verhulst-Pearl and Gompertz models have been widely used, not only to describe dynamics of biological population for which they were initially suggested, but also to provide a mathematical formulation of engineering, economic, chemical, and environmental processes. The models have become a foundation for many other models.
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