Exponential Growth and Decay

     I introduced exponential growth to my Algebra students with a bit of a scenario. I offered to sell someone in the class my diamond wedding band. Of course this was met with a mixture of, "Why do you want to sell your ring?" and "Oooo me! Me! Pick me!" I chose a "lucky" buyer and brought them to the front of the classroom. I then proceeded to tell them that I would only make one deal with them. They had to give me a penny today, two pennies tomorrow, four pennies the next day, and so on for just one month. Both of my classes had students that were willing to take that bargain. I even offered to help them calculate how many pennies they would owe me each day. By the time we got to day 30 we were well into the millions. This sparked questions about how it could be so much when we only started with 1 measly penny. (Enter exponential growth) Needless to say, I still have my diamond ring.
     The next day, I went around to check homework and a whopping 5 students had completed or even attempted the assignment. I was beyond frustrated with them because about this time last semester they all stopped doing their homework and couldn't figure out why their quiz and test grades were so low. After getting on my soapbox momentarily about the importance of turning in their assignments an idea struck me. I had planned exponential  growth examples that dealt with money in savings accounts and different rates of growth, but I decided that I needed a more tangible example. So I posed the question: If you have a 55% in my class right now, but plan on bringing it up 5% over the next 6 weeks would you have a 80% at the end? Many of the students said that they would have an 85% at the end. We were able to use our exponential growth model to test this theory and they were surprised to find out that the grade would still be a C. They were really excited about these problems and by the end of class everyone in the room had the hang of it and could even apply it to the financial problems I had planned. When I introduce exponential growth I think I will start with a problem like the growth problems, but see if they can figure out whether or not a student will pass. I hope this lesson served a dual purpose and I have way more than 5 people turn in homework!