In previous modeling lessons, students relied on the graphing calculator to find polynomial functions that fit a set of data. Lessons 20 and 21 comprise a two-lesson modeling exercise in which students model the shape of a riverbed in order to calculate flow rate of the river; this can be used to determine if the river is vulnerable to flooding. In this first lesson, students use the remainder theorem as a way to fit a polynomial function to data points without relying on technology.
In the second lesson, students use technology, particularly Wolfram Alpha, to find the equation of the interpolating polynomial that best fits the data. The online calculations through Wolfram Alpha can be done as a demonstration for the class or individually if students have access to computers. They can also be replaced by polynomial regression on a graphing calculator.
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