Exponential Functions Through Car Depreciation
Weapon of Math Instruction
10 Followers
Grade Levels
8th - 12th
Subjects
Resource Type
Standards
CCSSHSF-LE.A.1
CCSSHSF-LE.A.1a
CCSSHSF-LE.A.1c
CCSSHSF-LE.A.2
CCSSHSF-LE.A.4
Formats Included
- Word Document File
Pages
4 pages
Weapon of Math Instruction
10 Followers
Description
This is a group/individual activity where students get to see exponential decay in real life, understand why it happens, find growth rates, and practice calculating expected values. By the end of the activity, students will be ready to have a rich conversation about functions theoretically approaching zero. They will then have to rectify that theoretical truth with the reality of car values.
By the end of the project, students will be able to:
Define depreciation and relate multiple real-world examples to depreciation.
Define projected value.
Calculate a growth rate (or decay rate).
Predict and justify their ideal growth rate for the value of a car.
Calculate the projected value of a car after many different amounts of time.
Evaluate how long it will take for the decaying function to reach a value of 0.
**This activity works best saddled in between the introductory lesson to exponential growth & decay functions, but before students are asked to solve for variables abstractly. Since the entire project is based on real world, relatable scenarios, it offers multiple opportunities to critically think and check your work using common sense.
Detailed answer key sold separately, including suggestions for enriching discussions and places to incorporate graphing. Hope you and your students enjoy!
By the end of the project, students will be able to:
Define depreciation and relate multiple real-world examples to depreciation.
Define projected value.
Calculate a growth rate (or decay rate).
Predict and justify their ideal growth rate for the value of a car.
Calculate the projected value of a car after many different amounts of time.
Evaluate how long it will take for the decaying function to reach a value of 0.
**This activity works best saddled in between the introductory lesson to exponential growth & decay functions, but before students are asked to solve for variables abstractly. Since the entire project is based on real world, relatable scenarios, it offers multiple opportunities to critically think and check your work using common sense.
Detailed answer key sold separately, including suggestions for enriching discussions and places to incorporate graphing. Hope you and your students enjoy!
Total Pages
4 pages
Answer Key
Not Included
Teaching Duration
1 hour
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Standards
to see state-specific standards (only available in the US).
CCSSHSF-LE.A.1
Distinguish between situations that can be modeled with linear functions and with exponential functions.
CCSSHSF-LE.A.1a
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
CCSSHSF-LE.A.1c
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
CCSSHSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
CCSSHSF-LE.A.4
For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology.
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Questions & Answers
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