Overview: Over the next few weeks, we will consider two different population growth models. The first model is called the fixed percentage approach in which population growth can be modeled simply when we assume a fixed percentage of animals alive at one stage reproduce and add their offspring to the next stage. The second approach we will consider is called the carrying capacity approach. In this model we assume there is a maximum population that an area can support; this is known as the carrying capacity. We then define the current saturation, which we will call x, to be the fraction of the carrying capacity that the current population represents. We assume the population that reproduces at any stage is directly proportional to 1-x.
Prompt: Considering the scenario described above, describe in your own words the problem that the model must be developed to solve, why modeling is an appropriate way to find a solution to the problem, and what the most important factors within the scenario for the creation of a model would be. Please note what aspects of the scenario will help you determine which type of model you might build.
Be sure to include the following critical elements:
Introduction: What problem(s) or question(s) do you need to address? Explain why using mathematical models is an appropriate way to address the problem(s) or question(s).
Scenario Factors: What are the important factors to consider? What aspects of the scenario will help you in determining the appropriate type(s) of models to build?
The audience for this assignment is nonmathematical people and therefore should include clear explanations of possibly confusing concepts.
Peer Responses: Compare and contrast your peers’ justification for why using mathematical models is appropriate for this scenario with your own. What factors did you have in common with your peers, and what factors were different?
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