Lesson 1

Lesson 1: Characteristics of Exponential Functions

 

Focus

 

How can you describe the growth of certain populations or the decay of radioactive elements? It may be possible to describe some of these growths or decays with terms such as doubling, tripling, or halving. You may have heard about half-lives in science or exponential growth in finance, or you may have dealt with compound interest in the past. These are some examples of exponential functions in the world around you.

 

Do you enjoy energy drinks, coffee or tea, or pop? All of these drinks contain caffeine that is removed from the body over time. The time it takes to leave the body depends on the amount of caffeine consumed. Typically, the amount of caffeine in the body decreases by about half for each hour that passes. An example of a quantity that keeps decreasing by the same rate over a specific time is the mass of caffeine in a person’s body. The amount of caffeine decreases by about half each hour.

 

In this lesson you will examine quantities that are increasing or decreasing by the same rate over time. What would the graph of the mass of caffeine in a person’s body look like over time? Is there a type of function that can be used to describe this relationship?

 

Lesson Outcomes

 

At the end of this lesson you will be able to

• describe the characteristics of exponential functions by analyzing graphs
• describe the characteristics of exponential functions by analyzing equations

Lesson Question

You will investigate the following question: How can the characteristics of exponential functions be described using graphs and equations?

 

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 1 Assignment (Download the Lesson 1 Assignment and save it in your course folder now.)
• course folder submissions from Try This and Share activities
• additions to Glossary Terms and Formula Sheet
• work under Project Connection

Self-Check activities are for your own use. You can compare your answers to suggested answers to see if you are on track. If you are having difficulty with concepts or calculations, contact your teacher.

 

Remember that the questions and activities you will encounter provide you with the practice and feedback that you need to successfully complete this course. You should complete all questions and place your responses in your course folder. Your teacher may wish to view your work to check on your progress and to see if you need help.

 

Time

Each lesson in Mathematics 30-2 Learn EveryWare is designed to be completed in approximately two hours. You may find that you require more or less time to complete individual lessons. It is important that you progress at your own pace, based on your individual learning requirements.

 

This time estimation does not include time required to complete Going Beyond activities or the Module Project.