Intermath | Workshop Support

Write-up


Title

What type of a function is car depreciation?


Problem Statement
Identify the make and model of an automobile. Find the prices of various years of the model in a blue book. Find at least five ordered pairs (age, price) and plot all of the points describing the market value price of the automobile vs. the age of the automobile. Does this data best describe a linear, exponential, or quadratic relationship? Explain your reasoning.

Problem setup

The problem is to determine if the data collected of a car's yearly depreciation is a linear, exponential, or quadratic relationship. My first guess is that it would not be linear, that is, the car will depreciate faster with age.

 

Plans to Solve/Investigate the Problem

I will use the make, year and model of my own car to do the experiment, a 1996 Toyota Avalon. I plan to go the Edmunds Used Car Prices Link: Used Cars - Index and gather data for the depreciation of the car based on the years 1995 - 2002. I will then graph the data and determine what type of function it is.

 

Investigation/Exploration of the Problem

 

Click Here to create a spreadsheet

 

I recorded and graphed the data for the chosen years from the bluebook value off the web site using a spreadsheet. The graph appears to be more linear than exponential or quadratic. By determining the R2 of the graph as if it was exponential, the value is 0.9796 and the linear graph has an R2 of 0.9697, evidence that the graph is exponential. However, based on the data points I feel that the graph is only practicable within the range of the graph, predicting any car prices above or below the data points would have a large margin of error given the circumstances of depreciation. A new car is not going to cost, with the current rate of inflation, as much as the graph would suggest. Also, a used car will most likely reach a plateau and eventually as a classic car may ever rise in value over many years.

 

Extensions of the Problem

Possible extensions of the problem could include finding a car model that has been manufactured for several years, for instance, a Ford Thunderbird.

Author & Contact
Insert name and contact information.
Insert Email

Link(s) to resources, references, lesson plans, and/or other materials
Link 1
Link 2