Objective

Opening Discussion

Estimating the Age of a Vehicle

Auto Loans and Exponential Decay

Not your "typical" Homework Assignment...

Logs, Loans, and Life Lessons!

6 teachers like this lesson

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.

Big Idea

This engaging lesson weaves together logarithms, loans, and life lessons!

Lesson Author

Jarod Hammel

Huntington, IN

Grade Level

Subjects

Math

Algebra

Standards

HSA-SSE.A.2

Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).

HSA-CED.A.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

HSF-IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

HSF-IF.B.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*

HSF-IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*

HSF-IF.C.8b

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

HSF-IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

HSF-BF.A.1

Write a function that describes a relationship between two quantities.*

HSF-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).

MP1

Make sense of problems and persevere in solving them.

MP4

Model with mathematics.

MP5

Use appropriate tools strategically.

MP7

Look for and make use of structure.

MP8

Look for and express regularity in repeated reasoning.

Opening Discussion

15 minutes

Estimating the Age of a Vehicle

10 minutes

Auto Loans and Exponential Decay

10 minutes

Not your "typical" Homework Assignment...

10 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!

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