SWBAT write an exponential growth or decay function to model a given real world situation.

On day 1 students find percent increase/decrease and simple interest to establish a pattern which extends to writing exponential functions.

I found this lesson on the blog *Function of Time. *I love how the activity is designed to step students into modeling with exponential functions. The students work in a real world context that is soon to be applicable to our students. AND, the lesson is a deep exploration of the mathematics. Thank you to Blogger (Kate Nowak) for sharing such a great activity! Love it!

**Environment: **This credit card investigation is scheduled to last over 3 class periods (later revised to 4 class periods). I will outline how I plan to split this up, but of course it may not tie up as nicely as I would like each day. I am going to have students work on this activity ONLY to maximize class time. No clicker questions for warm-ups and closures. I really want them to focus on their work and make connections. We will summarize and close out the learning together daily. I want students working in teams to solve these problems and will be asking students to focus on **MP3: Construct viable arguments and critique the reasoning of others**. I plan to have whiteboards and markers available to students for scratch work and brainstorming.

**Blog Link**:

45 minutes

Part 1: Calculating Percent Increase/Decrease

The credit card investigation begins with students revisiting the topic of calculating percent increase/decrease. It is very important that students are able to do this using a one-step calculation. The skill and thinking required to do so helps them to write the exponential function in general form for the next section. Be sure to not rush students through this section. It is ESSENTIAL to students' success over the next four days that they understand how to calculate a percent increase or decrease using only a one-step calculation.

Part 2: Skipping Payments

During the skipping payments section, be on the lookout for students that get stuck while generalizing the pattern (in terms of x) at the bottom of the table. It may be helpful to guide students. They need to interpret the pattern in the table as an explicit operation based on any year, y, rather than a recursive function that is dependent on the prior year’s information. For example, if a student is trying to find the balance on year 5 with a 25% interest rate they should not rely on finding the year 4 information first. Make sure that your students understand the balance as the result of $1000 being multiplied by 1.25 five times.

I expect my students to specify the rate of change before identifying the function from a table of values. If necessary, I will help my students to recognize the process as repeated multiplication. I want them to be fluent with determining the percent rate of change.

5 minutes

Today's lesson may end a bit abruptly as students will be stopping work today on this part of the investigation, What is an Interest Rate, and picking up where they left off tomorrow. I found that after taking time to explore credit cards my students came up with a lot of great questions about credit cards. Why would you want a credit card? Are they good or bad to have? What is interest? Why do you have to pay someone to have a credit card? Is this like a loan when you buy a car?

I let these questions brew as my students worked through the day 1 investigation then addressed the questions at the end of class as a quick closure.

1 minutes

Assign worksheet #5 from this unit for homework. Students are just being asked to watch a 20 min podcast interview from NPR. So, students will need a computer and internet access to complete this assignment. It may be helpful to include this link on a class website or shared drive. You can also download the podcast from the NPR website so that students can upload it to their music players.