This is a great activity to use BEFORE teaching Exponential Growth and Decay. The students that succeed with this activity will be set up to ace the topic prior to it even being taught traditionally because they will have discovered how to do it all by themselves. The activity features two scenarios - one an exponential growth and one exponential decay - and asks students to figure out how to decode the growth and decay formula by manually adding 6% to a town's population (growth) or depreciating an airplane (decay) to find the value of either the town's population or the value of the plane per year through 20-50 years.
This task can obviously get tedious, but it demands that students try to find a "shortcut" to find the population or the value of the airplane after a decade or two decades' break in calculations. I almost always do this activity in groups of two or three so that the task doesn't appear as daunting, especially for those students that tend to shut down when a task is even remotely challenging. Also, depending on your group of students, it can easily be a two day activity.
There is a skeleton of the formula provided for the students within the worksheets. All they have to figure out is what goes in the blanks to make the formula work. It's easier said than done, though. The students that enjoy a challenge REALLY like this activity. I hope you will, too!!