Graphing Exponential Functions

📋 Course Outline

1. Exponential Function Foundations
2. Growth and Decay Models
3. Basic Exponential Graph Features
4. Transformations of Exponential Graphs
5. Piecewise Exponential Comparisons
6. Applications and Average Change
7. Analyzing Exponential Statements

📖 1. Exponential Function Foundations

🔑 Key Concepts & Definitions

• Exponential function: a function with the form $f(x)=b^x$, where the base b is a constant and the independent variable x is the exponent
• Asymptote: a line that the graph of a function approaches

📝 Essential Points

📌 An exponential growth function has base b>1, whereas an exponential decay function has base 0<b<1.

💡 Memory Hook

Growth uses b > 1, whereas decay uses 0 < b < 1.

📖 2. Growth and Decay Models

★ Must-know

📐 Formula — Exponential growth can be modeled by $A(t)=a(1+r)^t$, where A(t) is the amount after t time periods, a is the initial amount, and r is the percent increase per period.

📐 Formula — Exponential decay with an initial amount a and a decay rate r can be modeled by $A(t)=a(1-r)^t$.

Further detail

• The growth factor for an exponential growth model is 1+r.