Exponential Functions
Essential Question: How do we model and use exponential growth and decay?
Exponential Functions
1) Using Exponential Functions Word Problems
- Explanation:
- Notes | Answers
- 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)
- Worksheet #2
- Khan Exercise: Exponential model word problems
2) Finding and Using Basic Exponential Functions (y = a*b^x)
- Explanation:
- Notes | Annotated
- Websites:
- US Debt Clock
- CA Debt Clock
- Video:
- Khan: Modeling ticket fines with exponential function
- Khan: How to construct a modeling function according to half-life (example) (with exponent of t/n)
- Khan: Writing exponential functions from tables
- Practice Problems:
- Worksheet #1
- Worksheet #2
- Khan Exercise: Exponential functions from tables & graphs
- Algae Bloom
3) Exponential Functions When Given a Rate (y = a*(1+r)^t)
- Explanation:
- Notes | Annotated
- 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:
- Worksheet #1
- Worksheet #2
- Khan exercise: Interpret change in exponential models
- Khan exercise: Interpret time in exponential models
4) Compounded Interest
- Explanation:
- Notes | Annotated
- Khan videos:
- Introduction to interest
- Interest (part 2)
- Practice Problems:
- Worksheet #2
5) Using Continuous Growth or Decay Exponential Functions (y = a*e^(kt))
- Explanation:
- Notes | Annotated
- 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:
- Worksheet #1
- Worksheet #2
6) Finding Continuous Exponential Functions
- Explanation:
- Notes | Annotated
- Khan video: Thomas Malthus and population growth
- Practice Problems:
- Worksheet #1
- Worksheet #2
- Snail Invasion WS
- US Population Activity | Desmos version
- Town Population Project
7) Exponential vs. Linear Functions
- Explanation:
- Notes
- 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:
- Worksheet #1
- Worksheet #2
- 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)
- Worksheet
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