Understanding exponential growth and decay
Create and analyze a simple exponential function arising from a real-world or mathematical context.
Students have been introduced to exponential functions in A2. For some students this introduction could have occurred a year or two previously. Therefore this unit starts with an activity that re-introduces exponential growth and decay in an engaging real-world or mathematical context. The context can be modeled by an exponential function with domain contained in the integers, thus providing a review of previous experience as needed for students.
External Resources
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Green Acres
Description
WHAT: From the Mathalicious website: “Over the last two centuries, more and more people in the U.S. have been moving out of the country and into cities. The urban population, as a percent, has grown from about 6% in 1800 to over 80% by the end of the last decade. But the rate of growth hasn’t been constant. So how have cities been growing and changing over the past 200 years? In this lesson students use recursive rules and linear and exponential functions F-LE.A.1, F-LE.A.2 to explore urbanization in the U.S., as well as what different levels of urbanization might mean for future life in the country.”
WHY: This is a low bar/high ceiling lesson in an engaging modeling context MP.4 that can serve to re-orient students with prior learning about the nature of linear and exponential growth, approximating growth rate based on data, and building and interpreting functions. Many opportunities are presented to engage in constructing arguments MP.3. The last two questions invoke a recursive rule that offer a nice challenge if time permits.
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