What a Workout! 1 Copyright © 2026 Pearson Education, Inc. What a Workout! (50 – 60 minutes) Learning Objective(s): Students will use a graphical representation of a linear function to model a real-life situation and solve mathematical problems. Students will use multiple representations of exponential functions to model a real-life situation and solve mathematical problems. Material needed: Student pages: What a Workout! Lesson Procedure: Warm–Up 10 minutes Prompt: When have you planned a big project? What was the project for and what tasks did you complete? Discuss: Have students share with the group their experiences planning a big project, such as organizing a bake sale or a birthday party. Guided Instruction 15 minutes Present: scenario for What a Workout! Example: Functions can be used to model real-world situations. Two common types of models are linear models and exponential models. What are the similarities and differences between linear and exponential models? Sample answer: Both represent input on the x-axis and output on the yaxis. Linear models graph as a straight line; exponential models as a Jshaped curve. What key features can you look for on linear and exponential models? Sample answers: where they intersect the axes, average rate of change in the functions, whether they are increasing or decreasing Review: key terms – linear function, exponential function, model linear function: a function that increases or decreases by a constant difference as x varies exponential function: a function that increases or decreases by a constant ratio as x varies model: a mathematical representation of a real-life situation Independent Practice 20 minutes Distribute: student activity What a Workout! Have students first work individually and then discuss question 3 in pairs. Encourage students to support each other during the activity and be courteous during their discussions. Closure 10–15 minutes Review Answers: 1. a. 40; b. 80; c. Sample answer: I found $4 and $0 on the x-axis and followed the line up until I met the graph. Then I read the value from the yaxis for that point. 2. a. between $0 and $2; b. Sample answer: At those prices, the attendance at the class is expected to be more than 60 people, which would be beyond the capacity of the classroom. 3. a. M(x) = 200(1.2)x; b. Sample answer: I evaluated each of the equations at x = 1 and x = 4. Then I chose the one that had values closest to the values in the table. 4. B 5. Sample answer: No, because the models expect the club to grow indefinitely. Eventually, either the town will run out of people to join the club or the club will be too small to fit all the members. Discuss: How are linear and exponential models helpful for businesspeople who are making decisions? How can they help you make decisions?
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