Green Acres
How has the urban population of the U.S. changed over time?
In this lesson students use recursive rules and linear and exponential functions to explore urbanization in the U.S., as well as what different levels of urbanization might mean for future life in the country.
Students will
- Given a graph of real-world data, calculate potential linear and exponential rates of change
- Develop linear and exponential models for urban population growth and evaluate them for different years
- Informally compare the goodness-of-fit for the two models and use them to make predictions
- Given a recursive rule to model urbanization, compare and contrast its behavior to the previous models
- Vary the parameters of a recursive rule to achieve different long-term behavior
- Discuss how different urbanization trends might affect the future of life in the U.S.
Before you begin
Students should be able to describe the difference between linear and exponential functions in terms of rates of change, as well as write explicit formulas based on those rates. Students will also be exposed to recursive rules, so some familiarity with that concept would be helpful, though this lesson could serve as an introduction.Common Core Standards
Content Standards
Mathematical Practices
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