Lesson plan

Understand continuous growth for any constant percent rate of change by exploring infinite sequences

teaches Common Core State Standards CCSS.Math.Content.HSF-IF.B.4 http://corestandards.org/Math/Content/HSF/IF/B/4
teaches Common Core State Standards CCSS.Math.Content.HSF-IF.C.8b http://corestandards.org/Math/Content/HSF/IF/C/8/b

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Big Ideas: Exponential functions grow by a constant percent rate per unit interval. This means that they change multiplicatively, and not additively. The sequence (1+r/n)^n converges to e^r for any percent rate, as n goes to infinity. In this task students, students use what they have learned in Task 8 and apply that learning to explore how the sequence given by (1+r/n)^n converges to e^r as n goes towards infinity. This helps to build the conceptual framework for understanding the formula for continuous growth given by A=Pe^rt, where A is the amount at time t, P is the principal amount, and r is the percent rate. Vocabulary: exponential, growth, constant, rate Special Materials: Calculator