Model periodic populations. Here, in the context of foxes and rabbits, pupils look at graphs of the populations of these animals in a national park over a span of 24 months. Groups analyze the graphs and determine trigonometric functions that could model the data. To finish, they find what points of the data are important to use in determining the parameters in their functions.

Concepts

math modeling, graphing trigonometric functions, trigonometric functions, trigonometry applications, trigonometric word problems, predator-prey relationships, predators, rabbits, parameters

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Additional Tags

math

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Instructional Ideas

• Gather all of the function models and graph them on the same axes; let learners determine which one models the data best
• As a class, decide on the maximums and minimums for each of the populations

Classroom Considerations

• Class members should know the relationship between a graph's properties and the parameters of a trigonometric function

Pros

• The key graphs the data and the function on the same axes to show how it fits
• Includes more realistic data that does not exactly fit the curve

Cons

• None

Common Core

HSF-TF.B.5