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### Exponential Functions

 Essential Question: How do we model and use exponential growth and decay?Exponential Functions1) Using Exponential Functions Word ProblemsExplanation:Khan video: Exponential model word problem: medication dissolve (the equation is solved by inverse operations; you can solve by graphing)Khan video: Exponential model word problem: bacteria growthPractice:Worksheet #1 (use desmos.com to graph the functions)Worksheet #2Khan Exercise: Exponential model word problems2)  Finding and Using Basic Exponential Functions (y = a*b^x) Explanation:Notes | AnnotatedWebsites:Video:Khan: Modeling ticket fines with exponential functionKhan: How to construct a modeling function according to half-life (example) (with exponent of t/n)Khan: Writing exponential functions from tablesPractice Problems:3)  Exponential Functions When Given a Rate (y = a*(1+r)^t)Explanation:Notes | AnnotatedWebsite: U.S. and World Population ClockVideo:Khan video: Exponential growth and decay word problems Khan video: Interpreting change in exponential modelsKhan video: Interpreting time in exponential modelsKhan video: Constructing exponential models: percent changeKhan video: Exponential and logistic growth in populationsPractice Problems:Worksheet #1Worksheet #2Khan exercise: Interpret change in exponential modelsKhan exercise: Interpret time in exponential models4)  Compounded InterestExplanation:Notes | AnnotatedKhan videos:Practice Problems: 5) Using Continuous Growth or Decay Exponential Functions (y = a*e^(kt))Explanation:Notes | AnnotatedKhan video: Introduction to compound interest and eKhan video: e and compound interestKhan video: Compound interest and e (part 2) Khan video: Compound interest and e (part 3)Khan video: Compound interest and e (part 4)Practice Problems:6) Finding Continuous Exponential FunctionsExplanation:Notes | AnnotatedVideos explaining the problem:Khan video: Thomas Malthus and population growthPractice Problems:7) Exponential vs. Linear FunctionsExplanation:Practice Problems:Worksheet #1Worksheet #2Khan exercise: Linear vs. exponential growth: from dataKhan exercise: Linear vs. exponential growth Khan exercise: Construct exponential models8)  Graph of Exponential and Logarithmic FunctionsExplanation:Notes (answers are on the last two pages)The Prudential Dominoes ExperimentKhan video: Exponential function graphKhan video: Graphs of exponential growthKhan video: Graphs of logarithms & exponentialsKhan video: Graphing basic logarithmic functionsExponential Growth with different bases (use the slider): websiteExponential Decay with different bases (use the slider): websiteExercise:Khan Exercise: Graphs of exponential growthKhan Exercise: The inverse relationship of exponents and logarithms (points on a graph, points on a coordinate plane, and re-writing equations)Worksheet9) Logarithmic ModelingExplanation:Khan video: Richter scaleExercise:10) Logistic CurveExplanation:Notes (answers are on the last page)Khan video: Exponential & logistic growthExercise:11) Review ExplanationNotesPractice Problems12) Cumulative Review Worksheet #2