## IMG_0333.MOV - Section 3: Auto Loans and Exponential Decay

*Log, Loans, and Lessons PPT.pptx*

*IMG_0333.MOV*

# Logs, Loans, and Life Lessons!

Lesson 14 of 21

## Objective: Students will be able to futher their knowledge of logarithms by applying them to dB's of sound. Students will compare sounds mathematically by using knowledge of exponential functions and logarithms.

*45 minutes*

This is a homework assignment that the students literally can’t wait to get started! I allow them to select their own vehicle, or “purchase” one from my “car lot” of cut strips from Cars.com. I ask the students to be sure to pick a vehicle between $40,000 and $70,000. In the assignment, the students are asked to graph the depreciation function for their automobile, as well as provide (and graph) a linear loan function that would be suitable for the purchase. Although I encourage them to experiment with other down payments, I require them to put at least 20% down on the purchase price. This is a really fun and insightful activity!!!

Question #10 tells the students to be prepared to share their results with other students and teachers. The next day, I like to put the kids in a situation where they can orally communicate their findings. I have also gotten emails from parents in the past who talk about how neat it was to see their teenager bring home homework… AND actually WANT to talk about it!

#### Resources

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Introduction to Exponential Functions - Rational Exponents
- LESSON 2: Real Number Exponents
- LESSON 3: A Conceptual Introduction to Exponential Functions: Collaboration, Questioning, and Financial Advice!
- LESSON 4: Discovering Solutions to Exponential Equations
- LESSON 5: An "Exponentially" Rewarding Battle!
- LESSON 6: Productive Struggle - A Pre-Spring Break Challenge of Exponential Functions
- LESSON 7: Compositions, Inverses & Role Play: Extending Concepts to Exponential Functions
- LESSON 8: Exponential Functions and Logarithms - Connecting the Dots
- LESSON 9: Exponentials and Logarithms: LOUD and CLEAR!
- LESSON 10: A Wrap on Logarithmic dB's and An Extension to Logarithmic Properties
- LESSON 11: Classroom Journey: Exponential and Logarithmic Properties
- LESSON 12: Laws of Logarithms and Real Applications
- LESSON 13: Calculator Boot-Camp and Solving Exponential Equations
- LESSON 14: Logs, Loans, and Life Lessons!
- LESSON 15: "Demystifying e" Day #1
- LESSON 16: Logs, Loans, and Life Lessons Collaboration Day!
- LESSON 17: FInal Discussion - "Demystifying e" PLUS Skills Practice with Logarithms
- LESSON 18: Elephant Tracks!
- LESSON 19: End of Unit Differentiated Problem Set
- LESSON 20: Differentiated Problem Share Out - Unit Review
- LESSON 21: Unit Review