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Lesson plan

Construct an exponential function using two points on an exponential curve

teaches Common Core State Standards HSF-LE.A.2 http://corestandards.org/Math/Content/HSF/LE/A/2
teaches Common Core State Standards HSF-BF.A.1.a http://corestandards.org/Math/Content/HSF/BF/A/1/a

Construct an exponential function using two points on an exponential curve

Big Idea: If a graph is known to be exponential, two points are needed to find the values of a and b in the function y = ab^x. This lesson builds on students' work with exponential relationships. They know what makes a relationship exponential and they how to identify the key features of the graph of an exponential function, relating the key features back to the explicit equation. In this task, students will be given the graphs of two exponential relationships with only two points identified. One of the graphs identifies the y-intercept while the other one does not. Students consider the information given in the graph and then conclude that they have two unknowns, a and b, to find in the equation y = ab^x, requiring two equations to determine the unknowns. This lesson builds toward determining whether or not an exponential curve is indeed the best fit for a given set of data. Vocabulary: exponential, common growth factor / constant multiplier, systems of equations Special Materials: Scientific calculator