What type of a function is car
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.
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.
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.
of the Problem
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.
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