Exponential Functions (Lesson 3.1)
Unit 3  Day 1
Learning Objectives

Recognize scenarios that depict exponential growth by identifying a fixed percent/factor; distinguish exponential growth from linear growth

Write an exponential function modeling a scenario involving growth or decay by a fixed percent/factor

Understand that an exponential function is a function in which a positive constant (b) is raised to a variable (x), where 0<b<1 represents exponential decay and b>1 represents exponential growth
Quick Lesson Plan
Experience First
For this experience, students will work through this Desmos activity: Game, Set, Flat. This will take them through the science behind the bounce of a tennis ball. Students will investigate whether certain bounces indicate if a tennis ball is good or bad. The International Tennis Federation has ruled that tennis balls must have a rebound height between 53% and 58% of its previous bounce height. This models an exponential relationship that the students will discover as they work through the activity.
For Slide 8 (#3), make sure students know to fill in the table and draw the graph for the heights corresponding to a good tennis ball according to the rules set by the Tennis Federation.
Formalize Later
This activity introduces the idea of exponential growth and decay. Ask the students to explain how the pattern in an exponential function is different than the pattern in a linear function. The students discovered the form of an exponential function with an initial value (a) and a growth factor (b), so be sure to connect those parameters to the values they got from the Desmos activity. Explain that the Desmos used estimates, so the “initial height” of the tennis ball will vary from student to student, but that they should all be around 4 since that’s where the ball was dropped from.
For #2c in the Check Your Understanding, students may see “decreases by 10% every hour” and associate it with exponential decay. However, phone batteries are already expressed as percentages, so if battery decreases by 10% per hour, then it goes down by a fixed amount (starts at 100%, then 90%, then 80%, etc.). This is linear, not exponential.