- Understand the structure/behavior of exponential functions in relation to linear functions. (Linear functions/arithmetic sequences change by a common difference. Exponential functions/geometric sequences change by a common ratio.)
- Understand the characteristics of exponential graphs and tables, including how these characteristics appear in equations.
1 What happens if growth is multiplicative rather than additive?
The bundle opens with a modeling task that builds on students’ understanding of linear growth and uses that understanding—along with a playful context—to launch into an informal exploration of exponential growth. The emphasis here is on tables and graphs.
2 What are the important properties of graphs of exponential functions?
Having seen exponential functions, possibly for the first time, students now have an opportunity in Polygraph: Exponentials to sharpen their understanding of the visual similarities and differences of linear and exponential functions.