Bringing it together
• Interpret graphs and expressions for exponential functions (F-IF.C.7e$^\star$, F-LE.B.5$^\star$).
• Model depreciation with linear and exponential functions(F-LE.A.2$^\star$).
• Compare linear and exponential models (F-LE.A.1$^\star$).
In this section, students bring together much of what they have learned in this unit. They use their ability to write linear and exponential functions given two input-output pairs, they compare different models, both linear and exponential, and draw conclusions from them.
WHAT: Students are given the value of different iPod models at different times, and construct both linear and exponential models for their value over time (F-LE.A.2$^\star$, MP4). They consider which model is most realistic (MP2). They also compare and contrast the depreciation of a few different Apple products, understanding the different depreciation rates and how they relate to each other.
WHY: The purpose of this task is to provide students with a real-world situation where both a linear or exponential model might be viable (F-LE.A.1$^\star$). Students examine and interpret the models (F-IF.C.7e$^\star$, F-LE.B.5$^\star$) and make an argument about which one is more realistic (MP3). They compare linear with exponential models, and they also compare different exponential models.
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