Learning Resources
Outcomes
In this lesson you will
- explore exponential functions of the form
where a > 0 and b > 0 - determine the effects of a and b on the resulting graph
- use the term asymptote
By the end of this section students will be able to:
- model real-world phenomena using exponential functions
- sketch graphs from descriptions, tables, and collected 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
Mathematical Modeling, Book 3 p.127 - 142
Section 01 introduced to you the simplest of the exponential functions 
; however, real world situations require a more complex version. You will now explore the exponential function of the form 
and discover how the constants a and b affect its graph. Keep in mind the transformation of functions that you have already encountered earlier in this course and earlier math courses since the procedures don't really change.
Towards the end of the section , you will have the opportunity to work with the function in the form 
and some simple real world applications.
This section should take 5 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- understanding of the meaning of zero and negative exponents