Objectives: To help students think carefully about the growth characteristics of exponential functions and to observe how these characteristics differ from linear functions.
Preliminaries/Lead-In: I will introduce this activity 5 - 10 mins before the end of the class before I would like to get working on it. I will talk to the students about the first page and ensure that they understand what we mean by calculating ratios of successive y-values. Then I will ask them to complete Q1-5 before the beginning of the next class.
Suggested Procedures: I will begin by discussing Q6 as a class based on their work on Q1-5. Then I will talk a little about the Fruit Fly example highlighting that we are going to try to build an appropriate modeling function for this data. Then I will ask them to work on Pg 8 while walking around and seeing what they are coming up with - I don't think I will come back to whole class discussion until everyone has at least tried to make some of the predictions asked for at the end of that page and preferably not until everyone has gotten through all of it. Depending on time and what I have seen walking around I might ask for someone to share work on the doc camera). Then I will let them work again in small groups on the first half of page 9. Once everyone has decided on a percent growth per day then I will work with them as a class on the document camera to build our model together and relate it back to the work they did on the compound interest activity. I am guessing that at that point I will definitely be out of time so if I get to there then I think I might send them home to finish the rest of it - if I am very far off of that then I may have to extend work into the next class.
Wrap-Up/Take-Away: We have developed an exponential model for this data and seen that it is a good model by plotting on Mathematica.
Possible Homework: If we are as far as the end of Page 9 then I might send them away with the rest of it.
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