It can be hard to make exponential decay relevant for students - there are only so many times you can talk about the half-lives of radioactive isotopes. Today, we’ll walk through how you can make exponential functions engaging with cars, money, and candy. 

Activity 1: Car Depreciation

In MATH: Depreciation of Car Value, students use the exponential decay formula to model how a car decreases in value due to depreciation over time. 

Using the Edpuzzle video and example problem, students learn how to evaluate word problems with exponential decay, including calculating decay rate. Then, they practice similar word problems and create a graph of car value over time. 

Activity 2: Purchasing Power

In MATH: Exponential Decay in Purchasing Power, students learn how inflation impacts how much they can buy with their money. Start with the Edpuzzle video, which illustrates why stashing your money in the garage isn’t always a great idea. Students learn what inflation is, review exponential decay vs. growth, and calculate the present value of $100 from 8 years ago.

Then, students practice using the exponential decay equation. They consider the present value of uninvested cash, stagnant salaries, and periods of high inflation. 

Building Engagement and Conceptual Understanding

Here are some fun ways you can supplement this activity to differentiate and deepen math learning.

• CREATE: Exponential Patterns Jigsaw (NGPF) uses visual patterns to explore exponential change. 
• APPLICATION: Growth and Decay (NGPF) is a differentiated problem set that analyzes exponential growth and decay. 
• The Decay Curve of Twizzlers is an activity where students model decay by repeatedly cutting Twizzlers in half and arranging them to form an exponential decay curve. Here’s the student-facing worksheet that was shared during a session by the Thomas R. Brown Foundation.
• Predicting Movie Ticket Prices (Desmos) is an interactive that also teaches exponential decay through inflation, as students learn how to model movie prices over time. 
• Marbleslides: Exponentials (Desmos) is another great Desmos interactive to strengthen the connection between exponential equations and their graphs. 

Extend the Personal Finance Learning

If you’re a math teacher, consider using these resources to learn more about personal finance and continue making real-world connections in math!

• VIDEO: Understanding Inflation (Red Canoe Credit Union)
• ANALYZE: Understanding Inflation (NGPF)
• MOVE: Inflation Over Time (NGPF)
• FinCap Friday: Deals on Wheels (NGPF) 
• FinCap Friday: Cars During Covid (NGPF)

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About the Author

Kathryn Dawson

Kathryn (she/her) is excited to join the NGPF team after 9 years of experience in education as a mentor, tutor, and special education teacher. She is a graduate of Cornell University with a degree in policy analysis and management and has a master's degree in education from Brooklyn College. Kathryn is looking forward to bringing her passion for accessibility and educational justice into curriculum design at NGPF. During her free time, Kathryn loves embarking on cooking projects, walking around her Seattle neighborhood with her dog, or lounging in a hammock with a book.