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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.
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.
Open Exponential Functions.
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.
Save your responses in your course folder.
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?
If required, save a record of your discussion in your course folder.