Lesson 6: 7-7 Writing Exponential Functions
Duration of Days: 4
Lesson Objective
Write exponential functions by using a graph, a description, or two points.
Solve problems involving exponential growth and decay.
What happens to the value of y as x approaches negative infinity?
How can you check that your equation is correct?
Based on the graph, is b>1 or is 0<b<1?
What is the general form of an exponential function?
What is exponential growth? What is exponential decay? What is compound interest?
Compound interest
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
See below
Exponential growth can be modeled using the general equation y=a(1+r)^t, and exponential decay by y=a(1-r)^t, where y is the final amount, a is the initial amount, r is the rate of change expressed as a decimal and r>0, and t is time. Compound interest is an example of exponential decay.
When Jing May was born, her grandparents invested $1000 in a fixed rate savings account at a rate of 7% compounded annually. Jing May will receive the money when she turns 18 to help with her college expenses. What amount of money will Jing May receive from the investment?
Remind students that in growth and decay equations, the amount inside the parentheses will be greater than 1 for growth and less than 1 for decay.
If students need a challenge, then ask students to write their own exponential growth or decay problems, using data from periodicals or the Internet. Have students share their problems with the class when they are complete.
Practice: Exercises 1 -8
Exercises 35-42