Use student knowledge of linear functions, their pattern and structure, to introduce exponential growth functions. With this activity students will compare linear growth to exponential growth and understand why exponential growth eventually increases faster. Students will use linear patterns to understand exponential patterns as percent increase.
As a lesson opener to this activity - and another means of re-enforcing the concept - I open the class today with the common cold virus papers. I put several of them around the room upside down on desks and in the floor so students who pick them up and read it realize they are now about to become sick. I use the timer on my phone track the growth every two minutes and we keep a running total of the virus strands in their bodies on the board during class. By the end, we write a function rule to model the total strands as a function of time.
Give students the activity page and allow them to work through the questions with a partner or a small group. Move about the room guiding student thinking with good questioning. Students generally see the pattern through the comparison and by using their knowledge of linear patterns to understand exponential patterns. Call students to the board to demonstrate the answers and explain the relationship between linear and exponential growth. That is the goal of this lesson to see how closely related the two types of functions are and how making only one adjustment changes the outcome dramatically when given enough time to grow (exponential will always grow more quickly when given enough time).