Objectives: For students to use their prior knowledge about compound interest to build exponential functions and to understand what the different quantities in an exponential function mean.
Preliminaries/Lead-In: I will remind them of percentages and how exponential notation works before we begin this activity.
Suggested Procedures: I will get them started on this in class allowing them to work through this activity with very little whole class discussion. I will walk around the classroom, check that they are coming up with the right generalizations and take the opportunity to talk to any groups who are confused. The main thing to notice in this activity is that all of the general functions we come up with have the variable in the exponent - a defining feature of an exponential function! There is also an opportunity to talk about functional notation again here - what do we mean by A(224)?
Wrap-Up/Take-Away: What effect does changing the initial amount, interest rate, compounding period etc have on the function we develop for the general situation? I will probably point out a few of these things together as a class but possibly not until the beginning of the next class.
Possible Homework: I will send them home to finish anything that they do not get through in class and either collect it or check off that they have completed it during the next class.
Follow this link to share with us how this activity (the original or your adapted version) worked in your classroom! Thank you for all of your feedback.
Alternative Versions:
If you make any adjustments to this activity we would appreciate you sharing your new version! Please save it as "YOURNAME Course Activity ....." and attach it below. Thank you!