In this lesson, you will analyze the graph of an exponential function $f$ given by $f(x)=a·b^x$. In particular, you study the effect of $b$ on the shape of the graph. To observe how $b$ impacts the shape of the graph when $b>1$ and when $0<b<1$, you simultaneously examine several functions of this form, all of which have the same value of $a$.

These lessons encourage greater attention to the growth factors of the different functions, rather than on interpreting the quantities in context. Since you are focusing mainly on understanding how varying $b$ impacts the graph, you are looking at the structure of an exponential function and its graph.

When you finish this lesson, you will be able to:

• Describe the effect of changing $a$ and $b$ on a graph that represents $f(x)=a·b^x$.
• Use equations and graphs to compare exponential functions.

Here are the activities that will help you reach those goals:

• 5.12.1: Modeling Exponential Decay
• 5.12.2: Equations and Their Graphs
  • 5.12.2: Self Check
  • 5.12.2: Additional Resources
• 5.12.3: Graphs Representing Exponential Decay
  • 5.12.3: Self Check
  • 5.12.2: Additional Resources
• 5.12.4: Possible Equation for a Function on a Graph

After these activities, you completed the following practice and review:

• 5.12.5: Practice
• 5.12.6: Lesson Summary