Exponential Functions
Essential Question: How do we model and use exponential growth and decay?
Exponential Functions
1) Using Exponential Functions Word Problems
Explanation:
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 growth
Practice:
Worksheet #1 (use desmos.com to graph the functions)
Khan Exercise: Exponential model word problems
2) Finding and Using Basic Exponential Functions (y = a*b^x)
Explanation:
Websites:
Video:
Khan: How to construct a modeling function according to half-life (example) (with exponent of t/n)
Practice Problems:
Khan Exercise: Exponential functions from tables & graphs
3) Exponential Functions When Given a Rate (y = a*(1+r)^t)
Explanation:
Website: U.S. and World Population Clock
Video:
Khan video: Exponential growth and decay word problems
Khan video: Interpreting change in exponential models
Khan video: Interpreting time in exponential models
Khan video: Constructing exponential models: percent change
Khan video: Exponential and logistic growth in populations
Practice Problems:
Khan exercise: Interpret change in exponential models
Khan exercise: Interpret time in exponential models
4) Compounded Interest
Explanation:
Khan videos:
Practice Problems:
5) Using Continuous Growth or Decay Exponential Functions (y = a*e^(kt))
Explanation:
Khan video: Introduction to compound interest and e
Khan video: e and compound interest
Khan 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 Functions
Explanation:
Khan video: Thomas Malthus and population growth
Practice Problems:
7) Exponential vs. Linear Functions
Explanation:
Khan video: Constructing linear and exponential functions from graph
Khan video: Constructing linear and exponential functions from data
Khan video: Linear vs. exponential growth: from data
Khan video: Linear vs. exponential growth: from data (example 2)
Khan video: Exponential vs. linear models: verbal
Practice Problems:
Khan exercise: Linear vs. exponential growth: from data
Khan exercise: Linear vs. exponential growth
Khan exercise: Construct exponential models
8) Graph of Exponential and Logarithmic Functions
Explanation:
Notes (answers are on the last two pages)
The Prudential Dominoes Experiment
Khan video: Exponential function graph
Khan video: Graphs of exponential growth
Khan video: How to plot points of a logarithmic function that corresponds to the inverse exponential function (example)
Khan video: Graphs of logarithms & exponentials
Khan video: Graphing basic logarithmic functions
Exponential Growth with different bases (use the slider): website
Exponential Decay with different bases (use the slider): website
Exercise:
Khan Exercise: Graphs of exponential growth
Khan Exercise: The inverse relationship of exponents and logarithms (points on a graph, points on a coordinate plane, and re-writing equations)
9) Logarithmic Modeling
Explanation:
Khan video: Richter scale
Exercise:
10) Logistic Curve
Explanation:
Notes (answers are on the last page)
Khan video: Exponential & logistic growth
Exercise:
11) Review
Explanation
Practice Problems