As highly successful independent mathematical and scientific technical contractors, celebrating the successful completion of your largest contract to date, you have just received a new contract -- clearly a direct result of your past success. The letter you received from Chemproc, Inc. (recently purchased by the MPC, Inc. conglomerate) on the subject of their recently initiated chemical processing factory follows.
8 Oct., 1995
Independent Mathematical Contractors, Inc.
Suite 2, Strawmarket Business Plaza
Lonlinc, SK 04685
As you know, Chemproc, Inc. has recently opened a chemical reprocessing plant in East Lonlinc. After an immensely successful start, we are beginning calibration and fine-tuning of the second of our four reprocessing lines. This line is concerned with the reclamation of gold from waste-chemicals produced by other companies -- which then contract with us to recover the gold. (The gold is used as a catalyst for the reactions with which they are concerned, and can be reused if properly extracted.) However, there are two technical issues about which we are contacting you that must be resolved before we are able to begin operation of the line.
First, we are in the process of purchasing the chemicals that we use in this reclamation and need to determine which of these is the most effective. We obtained for demonstration purposes a sample of the chemicals being offered by each of three different suppliers, and ran our reclamation line using these samples to determine which produced the best results.
The results of this test run are given in the table which follows; this was compiled by our consulting scientist, Dr. Gavin LaRose (recently hired from the private art sector by way of the enticement of a large industrial salary). It gives the amount of gold reclaimed as a function of time. To facilitate the run, we did not restart the line with each different chemical sample -- instead, we ran it with the first sample, waited briefly for the chemical to clear, and then added the second, etc. The first chemical was added at time 0, the second at the 5 minute mark, and the third after 10 minutes.
In order to determine which of the suppliers we should deal with, we need to know several things based on this test. We need to know which supplier's chemical was the most effective, and we need to know which produced the greatest reclamation rate when working at its peak efficiency---for, as you can tell from the data, the reclamation rate varies with time even while a single chemical is being used. The results that you obtain should be quantitative (numerically substantiated).
Second, Dr. LaRose has determined that the amount of gold reclaimed
as a function of time is approximately given by the formula
where a is the total amount of gold reclaimed using the chemical in question, b and c are constants determined by the chemicals used in the reaction, and $t$ is given in seconds. Based on the data with which we have supplied you, we need to know the correct values for these constants, and then, based on the resulting model R(t), how long it will take for 50%, 90% and 99% of the reclamation to take place. We need this information for the two chemicals giving the best results (as determined by your earlier investigation).
As specified in your contract, your report should be submitted by the 27th of this month so that we are able to begin full operation of the line by November (and therefore impress our stock holders). If you should find in the course of your investigation that you have questions regarding this project, you are to contact Dr. LaRose with the other members of your investigative team; he will be more than willing to assist you. You should further contact him (also as a team) by the 17th to report on your progress.
We look forward to seeing your finished report, which should conform to the enclosed technical report requirements.
E. Idu Pont, President
Encl: technical report requirements
: If it should prove useful, Dr. LaRose can provide you with a soft-copy of this data.
Technical Report Requirements
It is of paramount importance that the reports submitted to Chemproc, Inc. be written so that all members of the board of directors can understand and apply the information contained therein. These board members are all experts in their respective areas of chemical processing, but for their mathematical background should be assumed only to remember algebra and precalculus.
Reports should further:
last modified on 29 Feb 1996Gavin's Calc I Project 2, Fall 95