There is a lot on the web for students to model and explore exponential growth patterns. A quick web search pulled up a lot of options for me. I really liked this one: m&m lab. Just be warned you need a lot of m&m’s. Some groups had populations over 400. I placed the students in pairs or groups of 3. Any more than this I feel would be very unproductive for some members. This was a great way to demonstrate how the growth pattern was produced by a constant (or near constant) multiplicative change as apposed to a constant additive change brought by linear growth patterns. I will emphasize this again as the class moves towards learning about sequences and series.