Final Project for MATH 170
This project is designed to be open-ended, allowing you to go in whatever direction you feel is
most appropriate. The project centers on the future of fossil fuels on earth. There are four parts to
the project, described below. There are resources and information at the end of the description of
the project. During the rest of the semester, you will hand in regular progress reports on your
project. See Blackboard for the deadlines for these progress reports. The final project report
(individual papers) will be due at the end of the semester, when you take the final exam. For this
project, you will work in teams of three students each.
Essential Question to be Investigated
How long will the earth’s oil reserves last?
Presenting Your Results
You will present the results of your work individually in a typed report. This report should be
organized into sections, as described below. Where possible, use complete sentences in proper
grammar, graphs, charts, tables, and calculations to support your work. Be sure to provide proper
documentation skills (both in text and in a short bibliography, using either MLA or APA format)
whenever you make use of outside information. The audience for your report should be the
informed, but not necessarily scientific public. In other words, you need to write your report so
that any reasonably intelligent person could pick it up and understand what you have done, why
you have done it, and what you have discovered about the problem. The report should not
assume that the reader knows any specific information about the problem or about the
mathematics involved.
9 Title page: Include a title for the project (not “Final Project”; be descriptive), your name,
the date you are handing the project in, and the class (Math 170 Introduction to
Mathematical Modeling). Also include the names of the members of your group.
9 Description of the problem: Explain your understanding of the problem.
9 Part one results: Summarize the assumptions, calculations, and results from part one.
9 Part two results: See the description of part two for how to organize this part.
9 Part three results: See the description of part two for how to organize this part.
9 Part four results: See the description of part two for how to organize this part.
9 Conclusions: In this section explain your answer to the essential question posed above
and compare the answers obtained at each stage of the modeling process. You will have
one rough estimate (from part one), a refined estimate (from part three, based on work in
part two), and a further refined estimate (from part four).
9 Group evaluation: Write a brief summary of how the group performed in working on this
project. Explain what each group member did on the project.
9 References: Complete bibliographic references in either MLA or APA format go here.
9 Appendix: Calculations (by hand is okay, if you can’t type them; but I would prefer you
to use MS Word’s equation editor) go here. Make sure that each calculation is numbered
so that you can refer to them in the body of the report.
Part One: Preliminary Analysis Based on Naïve Assumptions
For this part, you will calculate the approximate number of years the oil supply
present on the earth will last using some pretty naïve assumptions. Most engineers
and scientists call such calculations back of the envelope calculations. They are crude
estimates that put some bounds on possible answers to the problem being
Final Project for MATH 170
investigated. Under the assumptions below, it appears that the earth’s oil will last approximately
15 billion years. Calculate the exact figure (to two decimal places) from the assumptions below.
Use Excel to make your calculations easier; this is especially important when for the next part of
the project, so set up formulas and make use of parameters in those formulas.
9 The entire earth’s crust is made of crude oil, available and accessible for refining into
automobile gasoline.
9 All oil use is through automotive gasoline.
9 All vehicles on the road make use of gasoline for fuel.
9 The number of vehicles on the earth right now is fixed for the entire future.
9 Each vehicle on the road drives about 10,000 miles each year,
9 The average gas mileage of a vehicle is 50 miles per gallon.
Part Two: Improving the Accuracy of Your Calculations by Refining the Model
Now you and your group members will work together to refine your analysis of the problem.
Any of the assumptions in part one can be challenged and refined. For this part of the solution,
you will each work on modeling one of the three aspects of the problem listed below with subquestions. This section of your report should contain three sub-sections, one for each aspect of
the model that is under investigation. In each of these sub-sections, you should first explain how
you think the modification will affect the final answer (how long will the oil last) and then
explain the work done to model this aspect of the problem. Your models for this part should
include diagrams of some sort (flow diagrams, for example), references to the data you used to
develop the model, the equations you are using (based on the flow diagrams), and some sample
output from Excel, either in the form of a graph or an abbreviated table of data.
A. How much of the earth’s volume is actually oil? How much of this can we reach and
refine into automobile fuel? How much oil have we already used up?
B. Is 50 mpg a realistic assumption for gas mileage? Do all types of vehicles have the same
gas mileage? How has gas mileage been changing over time? For this, you should
probably create a model, possible different models for different classes of vehicle
(commercial trucks, SUVs, passenger cars, etc.)
C. How does the number of cars and other vehicles changing over time? You may need to
model these using different types of vehicles, as in (B) above.
Part Three: Combining the Work
In this part of the report, you should take the work from part two and work together in your
group to combine it into a single spreadsheet/model for the oil consumption. Explain your work
and how you brought it all together into a single model. Explain the answer that you get as a
result of this. Include the diagrams and equations that you are using, as well as Excel output.
Part Four: Further Refinement
You and your group should generate a list of at least four different things you could modify in
the assumptions of the model. For each of these changes, you should describe (a) what the
change is and why you think it would be important and (b) how you think this change will affect
the ultimate answer to the question of how long the oil reserves will last. This section of the
report should contain about one paragraph for each of the four modifications. Each of the
Final Project for MATH 170
members of the group will then select one of these changes to make (a different one from all the
other members of the group) and will implement this change in the model and report on what
you did, how it affected the final result, and how this compares with your original expectations
regarding the change.
Some Resources
9 Conversion tables/calculations for any units are available from the site
www.onlineconversion.com.
9 Information on automobiles worldwide is available from
www.bts.gov/publications/nts/index.html, but you will need to make some assumptions
about the number of SUVs, minivans, and pickups, since these are not included in the
data tables. Be sure to spell out the assumptions your group makes.
9 You can learn about the process of oil refining from www.howstuffworks.com. This will
help you determine the amount of gasoline you can get from a single barrel of oil, as well
as the size (gallons or liters) of a barrel of oil.
9 If you need other information (like the size of the earth and the thickness of the earth’s
crust) can be found by asking questions at www.askjeeves.com.
9 You are free to use any other text or Internet sources available; be sure to provided proper
documentation in the report.
Further Advice on the Project
9 Remember your units. Save you they can.
9 You may want to look up the formula the volume of a sphere to help out.
9 Don’t bite off too much at once. If, for example, you want to create an
accurate model for the number of vehicles over time, start simple (all
cars are the same type, for example), work it through, and then try a
more complex model (different models for SUVs, trucks, etc.).
9 Make use of your team effectively (See advice below)
9 Don’t be afraid to come talk to me and ask questions in my office!
Grading of the Project
The final project is worth 15% of your overall grade (150 points – this is a correction to the
syllabus). The grade on the project is a letter grade (A, B+, etc.) and will be based on the
following components. More details will be posted on Blackboard.
9
9
9
9
Your communication skills in presenting the report
Your use of Excel and other technology to help solve the problem
Your analysis of the assumptions and modeling of the different parts of the problem
Your ability to use the modeling tools of the course in order to solve the sub-parts of the
problem
Final Project for MATH 170
More Information on Groups and How Not to Work Together
A team’s effectiveness is most often diminished because of a member(s) failure to make
meaningful contribution to the team effort due to one of the following types of behavior:
1. Inappropriate socializing
This limits others’ opportunities to learn due to distraction and the wasting of valuable
time.
2. Lack of class preparation
This usually means that the member has not kept up with the daily assignment(s), a
situation that almost always leads to free loading.
3. Free loading
A student habitually lets others carry the team discussion without making meaningful
contributions or does not seem willing to learn. This causes resentment in the other team
members, which may result in their justifiable reluctance to share ideas.
4. Absences
The team’s effectiveness is weakened by the loss of valuable input and its progress can
be seriously impaired when it must spend valuable time “catching up” the returning
member. Absences have a far greater adverse effect in a group-work class than in a
traditional lecture class.
5. Unwillingness to help other students
Almost always, this happens because the unwilling member is retaliating in response to
other members’ lack of meaningful participation.
6. Authoritarianism
A student does not listen to others’ contributions, seeks to dominate the group, is
unwilling to negotiate different viewpoints, or claims his/her ideas are correct without
providing adequate mathematical justification or support. Conflicting viewpoints and
argumentation are at the center of good teamwork. It is when viewpoints are
dogmatically inflicted on others without the support of proper mathematical reasoning
that problems arise. Authority becomes the arbiter of acceptance, not mathematical truth.
7. A marginal mathematical background
The student can overcome this situation if his/hers background is not actually inadequate.
That is, a person can do a lot of catching up if he/she is willing to work extra hard and
seek outside help from me, the Math Center, your Peer Associate assigned to this class, or
from classmates. A person with a marginal background can nevertheless be a
contributing member of the team if he/she can keep up with the assignments and remain
fully engaged in the course by extra preparation and help seeking. In this event, he/she
can ask meaningful questions during group work, seek clarifications from others, and
otherwise promote good mathematical discourse and group interactions.
8. Social Issues and Diversity
St. John Fisher College and your instructors are dedicated to providing an environment
that encourages and promotes diversity. Group members that act in ways that denigrate
and/or discourage students based on gender, social status, ethnicity, or ability will not be
tolerated.