Outcomes
In this lesson you will
- Explore exponential functions of the form
. - Determine the effects of a and b on the graph of .
- Discover the meaning of and work with asymptotes.
By the end of this section you should be able to:
- Model real-world phenomena using exponential functions.
- Sketch graphs from descriptions, tables, and collect data.
- Describe and translate between graphical, tabular, written, and symbolic representations of exponential and logarithmic relationships.
- Demonstrate an understanding of how parameter changes affect the graphs of exponential functions.
- Analyze scatter plots, and determine and apply the equations for the curves of best fit, using appropriate technology.
- Demonstrate an understanding of the role of real numbers in exponential and logarithmic expressions and equations.
- Analyze and describe the characteristics of exponential and logarithmic functions.
Introduction
In this section you will be introduced to exponential functions of the form 
and discover how the constants a and b affect the graph of the function.
Also in this section you will discover how to find the equations of exponential functions of the form 
for some simple real-world phenomena.
This section should take you about 5 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- The meaning of zero and negative exponents.
- How to generate a table of values for a function.
- How to graph a function using a table of values.
- How to use graphing technology to draw the graphs of functions.