Lesson 1: Exponential Functions
Focus
How can you describe the growth and decay of certain elements? One way is to say that an amount has doubled, tripled, halved, and so on.
An example of a quantity that keeps decreasing by the same amount over a specific time is the mass of a radioactive isotope. A radioactive isotope is a chemical element that is unstable and breaks down or decays into other elements. The time it takes for the element to decay to half its original amount is called the element’s half-life.
A medical isotope is a safe radioactive substance used primarily to diagnose illness. The energy emitted by the isotope when inside a patient is detected by special cameras while the patient is being scanned. These scans essentially light up the organ and show how the organ is working rather than what the organ looks like. The branch of medicine and medical imaging that uses these isotopes is known as nuclear medicine.
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In Canada, about one out of every three patients entering a hospital will undergo some form of nuclear-medicine procedure.
In this lesson you will examine quantities that are increasing or decreasing by the same amount over time. What would the graph of the mass of a medical isotope look like over time? Is there a type of function that can be used to describe this relationship? If so, how can you use these types of functions in other applications?
Lesson Outcomes
At the end of this lesson you will be able to
- sketch a graph of an exponential function
- apply transformations to the graph of an exponential function
- identify characteristics of the graph of an exponential function
- solve problems involving exponential growth or decay
Lesson Question
You will investigate the following question:
- How can exponential functions be graphed and analyzed?
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 have difficulty with concepts or calculations, contact your teacher.
Remember that the questions and activities you will encounter provide you with the practice and feedback 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 30-1 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.