Lesson plan

Understand how to recognize and build an exponential function by looking for patterns

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

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Big Ideas: In exponential functions, each successive term is found by multiplying the previous term by a constant multiplier Exponential functions can be written in the form y = ab^x where a gives the y-intercept and b is the constant multiplier This lesson builds on students' ability to write exponential functions given a description or a set of data in the form of a table. In this task, students will be presented with two seemingly unrelated situations in which students begin by writing estimates for what they expect the solutions to be. Students then develop explicit function rules for the data and examine how the actual function values compare to their initial estimates. Students will then look for what these two situations have in common and what makes them exponential. They will also look for clues within each problem that will aid in writing the explicit function rule. The mathematical concepts in this lesson build towards using exponential equations to solve problems and developing properties of logarithms that will help in solving exponential equations. Vocabulary: Explicit rule, Exponential, Constant Multiplier, Initial Value Special Materials: Calculator