In this lesson, you will analyze the graph of an exponential function given by . In particular, you study the effect of on the shape of the graph. To observe how impacts the shape of the graph when and when , you simultaneously examine several functions of this form, all of which have the same value of .
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 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 and on a graph that represents .
- 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