05.02 Exponential Situations as Functions

unit 5

Exponential Situations as Functions

 Goal

You will examine relationships - in descriptions, tables, equations, or graphs - and function notation that represents exponential relationships. Then, apply that knowledge by answering questions. 

  Estimated completion time: 40 minutes

 Watch

The situations we looked at that are characterized by exponential change can be seen as functions. In each situation, there is a quantity—an independent variable—that determines another quantity—a dependent variable. They are functions because any value of the independent variable corresponds to one and only one value of the dependent variable. Functions that describe exponential change are called exponential functions.

For example, suppose t represents time in hours and p is a bacteria population t hours after the bacteria population was measured. For each time t, there is only one value for the corresponding number of bacteria, so we can say that p is a function of t and we can write this as .

If there were 100,000 bacteria at the time it was initially measured and the population decreases so that  of it remains after each passing hour, we can use function notation to model the bacteria population:

Notice the expression in the form of  (on the right side of the equation) is the same as in previous equations we wrote to represent situations characterized by exponential change.

Review the function notation infographics below.

Watch the following video about exponential situations.

 Apply

Click the Take the Quiz button to start the assignment.

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