Abridged Lesson Plan: Model My Car Depreciation
Title of lesson: Interpreting Parameters in Exponential Functions – Car Depreciation Modeling
Audience: 9th Grade Algebra I / Algebra I with Probability
Content Objectives: Interpret the parameters in exponential functions of the form a*(b)^x in a real-world context. Students will explore car depreciation models and describe the roles of initial value (a) and decay rate (b). Using tools such as Excel and Desmos, students will construct models, compare scenarios, and justify conclusions using mathematical reasoning.
2020 Alabama Course of Study (Mathematics):
Mathematical Practices:
Establish mathematical goals to focus learning (MP1).
Use and connect mathematical representation (MP3).
Facilitate meaningful mathematical discourse (MP4).
Pose purposeful questions (MP5).
Build procedural fluency from conceptual understanding (MP6).
Support productive struggle in learning mathematics (MP7).
Algebra I Standards:
A1.16: Interpret the parameters of an exponential function in context.
A1.18: Use technology to explore and compare linear and exponential models.
A1.20: Analyze real-world contexts using functions represented in tables, equations, and graphs.
Behavioral Objectives:
Students will:
Interpret and identify the meaning of the parameters a and b in exponential functions.
Use modeling tools (Desmos, Excel) to simulate car depreciation scenarios.
Justify conclusions about car value and purchasing decisions using exponential reasoning.
Prerequisites:
Understanding of exponents and exponential functions.
Basic familiarity with function notation and graphing.
Basic spreadsheet operations and willingness to explore Desmos
Materials
- Computers or Chromebooks
- Internet access for Desmos Activity
- Excel or Google Sheets
- Student worksheet (printed or digital)
Procedure:
Introduction:
Display a real-world question: “If you buy a car today, how much will it be worth in 5 or 10 years?”
Explain the purpose: to model car depreciation using exponential functions and interpret the results.
Engagement:
Define exponential function: V(t) = a(b)^t
Explain the meaning of "a" as initial value and "b" as rate of change.
Use Desmos sliders and Excel table to visually explore how changes in a and b affect the graph.
Lecture/Direct Instruction:
Work through a real depreciation model: V(t) = 19885(0.75)^t
Guide students in creating a spreadsheet with t-values from 0 to 10.
Graph the values and interpret trends.
Discussion & Application:
Compare two car models with different depreciation rates.
Have students determine which car holds value longer and why.
Work in pairs or small groups to model their own example using custom values for a and b.
Conclusion:
Students explain in writing what each parameter represents in context.
Present or submit a short justification for which car model is most cost-effective and why.
Key Questions:
What does the parameter "a" represent in a real-world exponential function?
What does the parameter "b" tell us about how fast something is increasing or decreasing?
How can we use technology to interpret patterns in data and make informed decisions?
*Assessment*
- Accuracy and completeness of Excel and Desmos tasks
- Clarity in worksheet explanations and parameter identification
- Participation in class discussion and exit ticket