Distinguish between situations that can be modeled with linear functions and with exponential functions.
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Interpret the parameters in a linear or exponential function in terms of a context.
Exponential Functions are fun to introduce to students. There are so many relevant examples. I have used these thwo examples to reinforce the power of the exponential function:
• How Folding Paper Can Get You to the Moon by Ted-Ed
• MythBusters- Folding Paper Seven plus times on YouTube
This set includes five activities that illustrate exponential functions. Students analyze the scenario, create a table of values, and graph the values.
Ideas for using the station cards:
1) Assign one activity to each group of students. After students have completed the activity, invite each group to explain their work. Ask students to identify commonalities and differences. Compile key attributes of exponential functions.
2) Assign one activity to pairs of students. Check their work. After completing the assigned task, invite students to create their own scenario that results in an exponential function. Give students one sheet of construction paper. Ask them to fold the paper in half. On the front of the card, write their own problem. Inside create a table and graph illustrating the problem. Swap cards in class.
3) Set up the first four activities around the classroom as stations. Give students the recording sheet. After students have completed the stations, use Activity 5 as an assessment.