Module 6: Exponents and Logarithms

 

Explore

 

This is a photo of a boy counting pennies on a bed.

Polka Dot/Thinkstock

In Try This 1 you worked with an example of exponential growth. You may have determined that after about three months, in week 12, Logan’s allowance would have been 4096¢, or $40.96.

 

The relationship that describes the growth of Logan’s allowance in cents, A, as a function of week, w, is A = 2w. You will notice that the variable w is an exponent; therefore, A = 2w is considered an exponential function.

 

An exponential function is a function in the form y = cx, where c is a constant, c > 0, c ≠ 1, and x is a variable.

 

tip

Different letters can be used to represent the base of an exponential function. A common form is y = bx. In your textbook and in this course, the letter c is used to represent the base, y = cx. This is to avoid confusion with the transformation parameters a, b, h, and k that were introduced in the first module on transformations.


 

In Try This 2 you will explore the graphs of exponential functions.

 

Try This 2

 

Open Exponential Functions.

 

 

This is a play button that opens Exponential Functions.



textbook

Using Exponential Functions, complete “Investigate Characteristics of Exponential Functions” questions 1 to 5 on pages 334 to 335 of the textbook. Use the slider to change the c-value.

 

course folder Save your responses in your course folder.

 

Share 2

 

With a partner or group, discuss the following question based on the graph you created in Try This 2:

 

How does the value of c affect the shape and characteristics of the graph?

 

course folder If required, save a record of your discussion in your course folder.