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Lesson Plan

Graph a system of linear and exponential equations and interpret regions of the graph in context

teaches Common Core State Standards CCSS.Math.Content.HSA-REI.D.11
teaches Common Core State Standards CCSS.Math.Content.HSF-LE.A.3
teaches Common Core State Standards CCSS.Math.Content.HSF-LE.B.5
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Big Ideas: Exponential growth functions will eventually always overtake linear growth functions. We can use graphs and tables to estimate where f(x)>g(x), where f(x)=g(x), and where f(x)<g(x). Students are introduced to two beetles, Paul and John, who are climbing up a cubicle wall. The height of each beetle at any given time, t, is modeled by two functions (one linear and one exponential). Students are asked to decide when the linear function is greater, when the exponential function is greater, and when they are equal. They are then asked to interpret what each of these means in terms of the context. Vocabulary: exponential function, linear function, intersection, system of equations
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