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Web Activities
CHAPTER 1 PATTERNS OF GROWTH: SEQUENCES
The Scenario
You are about to purchase your first car! To help you in your decision
making process, you will develop several mathematical models that can
be used to predict the purchase price of the used vehicle of your choice.
First determine the type of vehicle you would like to purchase, including
the make and model. For this activity, choose a make and model that has
been around for at least five years. Use the internet to browse through
a selection
of vehicles to help you make your decision.
Used Car dealers use a document called the "blue book" that lists
the suggested resale value of any vehicle, year by year. Use the listed
prices in the blue
book to determine the dealers retail price of your vehicle for the
past 5 to 10 years. (If you find that the vehicle you have chosen does
not date back at least five years, choose another.) You will need to convert
the values you found from U. S. dollars to Canadian dollars. Use today's
current exchange rate provided by the Bank
of Canada.
Developing Models
- Using the data that you found, determine the average difference between
the dealers retail price from year to year. Use this information to
create the general term of sequence that could be used to predict the
cars retail price for any given year.
- Using the data that you found, determine the average depreciation
rate between the dealers retail price from year to year. Use this information
to create the general term of sequence that could be used to predict
the cars retail price for any given year.
- Using the TI-83 Plus graphing calculator enter the data you found
for your vehicle into the list editor. Place the year of the vehicle
in List 1 and the dealers retail price in List 2. Determine the best
model to use as a predictor of your vehicles price for any given year.
Be sure to investigate models using linear, quadratic and exponential
regression.
- You now have created three different models that predict the retail
price of your vehicle for any given year. Of these three different models
decide which is the best.
Your Job
Create a report, that includes the following items:
- A picture
of your vehicle, along with an introductory paragraph stating the used
vehicle that you would like to acquire (including the make and model,
but not the year)
- A table of values describing the list blue book prices vs. the age
of the automobile in Canadian dollars.
- All calculations you used in developing the three models. Include
a hand drawn scatter plot and "the best" regression curve; a
regression equation and correlation coefficient.
- A paragraph explaining and analyzing the three different models you
created. You should concentrate on what the numbers represent and how
someone else could interpret this information. Identify which model
you feel is the best and include your arguments for choosing it.
- A printout of at least three sale prices of the automobile
(they do not have to be the same year) from a location within Yahoo's
advertisements. In separate paragraphs, describe whether each price
is too high, reasonable, or a good deal. If a price is not "reasonable,"
then explain how you could determine a fair selling price. You must
use the "best model" to present your analysis of each quote.
- Finally, determine how long you plan to keep the car if you want to
resell it when it is worth $2000. Show your work!
You must write a report of at least 500 words (approximately two
double spaced pages). You will be assessed on how well the report addresses
the criteria mentioned above.
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