Lesson plan

Solve continuous exponential growth problems by using natural logarithms

teaches Common Core State Standards CCSS.Math.Content.HSF-LE.A.4 http://corestandards.org/Math/Content/HSF/LE/A/4

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Big Ideas: The formula f(t) = f(0)e^(kt) applies to quantities that exhibit continuous exponential growth. Natural logarithms can be used to find the value of the growth constant k, when the initial amount, final amount, and the time it takes to reach the final amount are known. This lesson builds on students' previous work with solving for an unknown exponent in an equation are the natural number e. This task gives example populations that exhibit continuous exponential growth and takes students through solving for unknowns in the exponent by using natural logarithms. Students them use the equations to make predictions of future population sizes. This task prepares students for future work with exponential functions of base e and natural logarithmic functions they may encounter in more advance math courses. Vocabulary: exponential growth, e, base, logarithms, exponent Special Materials: Scientific calculator Graphing calculator (optional)