Objectives: To build, evaluate the quality of, and predict from an exponential model of data.
Preliminaries/Lead-In: I will probably remind students that they might want to refer to CA 3.1,3.2 during this activity.
Suggested Procedures: I will allow students to work very independently on this activity which means for most of them they will go through the entire activity using ratio of successive y-values to build their model without noticing that we don't have an input variable that increases by 1 each time! This is a great learning opportunity as students are often too fast to turn whatever I give them into a process and this stops them in their tracks. Also it's a mistake that they see so clearly with Mathematica - an opportunity to point out why we use Mathematica as a visualization tool in this class and for their project. At the point where they realize that their model does not fit I will probably start by sending them back to the end of CA 3.1,3.2 where we discussed different delta t values and see if that helps them. As more students get confused I will either find a student who correctly modeled and ask them to share how they did it (or multiple students) or I might lead a class discussion myself - I'll have to see how time is going. After that I'll send them off to finish the activity independently. Notice that all of our headings on this activity correspond to what we ask them to do on the project with their data.
Wrap-Up/Take-Away:
Possible Homework: Finish the activity for next class.
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