Math 105--Calculus I: Project 2, Fall 1997

An Oily Mess...

by Gavin LaRose (, Nebraska Wesleyan University, September 1997

©1997 Gavin LaRose (
permission granted to use and distribute free in an academic setting.

As eminently successful mathematicians working for the ever-busier mathematical consulting company, Independent Mathematical Contractors, you find yourselves confronted by your second contractual project (to your joy, it might be added). This one comes from the West Coast, showing that it pays to be known by other companies in a similar field---in this case, the large Dran think-tank.

DVI file of project
PostScript version of project

The letter from DRAN...

Dran Corp.

1 Dran Rd.
Gos Andies, IF

29 September 1997

Independent Mathematical Contractors, Inc.
Suite 2, Strawmarket Business Plaza
Lonlinc, SK 04685

Dear IMC:

As you know, the Dran Corporation is a large scale think-tank that analyzes all manner of real-world situations for our clients, much in the same manner as your company operates. Unfortunately, we have found it expedient to subcontract a number of our analysies on account of the recent elopement of a brilliant mathematician with our (we like to emphasize) Ex-CEO.

In this case, we are investigating the rate of oil extraction from a now-defunct oil field to gain insight on the progression of returns from such fields as they mature. We know for this field that it is now for all intents and purposes not yielding oil, and that since it was first drilled in 1967 it has yielded approximately 55 billion barrels of oil. In addition, the mathematician (c.f. above) we previously had working on the problem concluded that the rate of oil extraction from a field of this type is an exponential function of time.

Given this information, we are interested in describing the rate of yield (in barrels per day) of this oil field at arbitrary times in its useful life, as well as a similar description of the amount of oil extracted from the field. It is to obtain these that we have contacted your company. As is our custom, we have established a liason in the local scientific community whom you should contact with any questions you may have in completing this project. This is the enthusiastic Dr. Gavin LaRose, who begged to be allowed to complete the project on his own. Unfortunately, his fee was too high and we have therefore retained him only as a consultant. You should be in touch with him by the 6th and 16th of October with an indication of your progress, and your final 3--5 page typewritten report is due by the 27th of October. Please be advised that, owing to the large amount of oil-money that is riding on our obtaining a successful solution to this problem, any failure to meet these deadlines will result in a significant penalty of at least 15% of your grade.

We look forward to hearing from you.

W. R. N. Cristof'r
Consultant-in-Chief, Dran Corp.


Gavin's Calc I Project 2, Fall 1997
Last modified: Fri Nov 28 11:49:48 CST 1997
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