% (c) 1996 Gavin LaRose (glarose@NebrWesleyan.edu)
% permission is granted to use and distribute for free
% in an academic setting
% 
\input /home/glarose/lib/macros
\input psfig.sty
\font\headerfont=pnb10 at 15 truept
\font\sevenrm=cmr7
\def\longindent{\hskip 4in}
\def\logo{\longindent\vbox{\hrule
		\hbox{\vrule\vbox{\kern 3pt
			\hbox{\kern5pt \headerfont Lonlinc CPE}
			}}}}


\settabs\+\indent & \hskip .5in & \hskip 1.5in & \cr
 
\nopagenumbers
 
\centerline{\bf Math 105---Calculus I\quad Project 1}
\centerline{\bf a placid midwestern lagoon\dots }
\centerline{\sevenrm \copyright\ 1996 Gavin LaRose
(glarose@NebrWesleyan.edu), Nebraska Wesleyan University}
\centerline{\sevenrm permission granted to use and distribute in an
academic environment}
\bigskip
The Independent Mathematical Contractors (, Inc.) company, after a
year of successful operation, has just hired you in an expansion of
its base of mathematical consultants to meet its burgeoning list of
contracts.  The latest contract received is from the Lonlinc
(Skanabra) CPE (Council on the Protection of the Environment), and
regards the site of the old Lonlinc Paint company, under investigation
prior to its proposed sale to the world-wide MPC, Inc. conglomerate.
 
\vfill\eject
 
\logo

\longindent the Lonlinc Building\par
\longindent South 9th Avenue\par
\longindent Lonlinc, SK 08685\par
\longindent \par
\medskip
\longindent 6 September, 1996\par
 
\bigskip
\bigskip
 
\noindent Independent Mathematical Contractors, Inc.\par
\noindent Suite 2, Strawmarket Business Plaza\par
\noindent Lonlinc, SK 04685
 
\bigskip
\bigskip
\noindent
Dear IMC:
\medskip
\noindent
The Lonlinc CPE, as part of its mission to protect the citizens of
Lonlinc from environmental hazards posed by modernization and
industrialization, is required to investigate sites with possible
environmental contamination prior to their sale to new owners.
Recently the site of the old Lonlinc Paint company has become the
subject of a possible sale, resulting in our investigation of the
same.  As you may know, Lonlinc Paint produced paints from 1961 until
1979 (with over 50\% of its production coming in the years
1974--1978), at which point its owners without explanation abruptly
ceased operations at the plant.
\medskip
\noindent
Our investigation of the site, which began a number of years ago, has
determined the following information.  There is a large ``lagoon'' at
the center of the plant into which paint residue and waste chemicals
were flushed regularly in the course of Lonlinc Paint's operations.
The chemical contaminants from the lagoon have leached down to the
water table in the region, and are being transported in the aquifer
below the site toward the nearby Flatt River.  In order to determine
the threat this poses to local water supplies, we have investigated
the water contamination at a number of wells near the site.
\medskip
\noindent
The first three wells were drilled by the owners of Lonlinc Paint, and
it is from their records that we obtain the following data:
\smallskip
\+ & well & distance from lagoon & water table level (measured up from
a reference level) \cr
\+ & 1 & 500 ft  & 60 ft \cr
\+ & 2 & 700 ft  & 58 ft \cr
\+ & 3 & 1000 ft & 55 ft \cr
\smallskip
\noindent
(at the lagoon the water table is 70 feet).  In 1980 all three were
clean, while in 1986 contaminants were detected in the water at wells
1 and 2 but not 3.  In 1991 there was some discussion of the sale of
the site of the company, and, on investigation, we found contamination
in well 3, and drilled an additional well, well 4:
\smallskip
\+ & well & distance & water table \cr
\+ & 4 & 1200 ft & 49 ft \cr
\smallskip
\noindent
In 1991 this well was not contaminated.  This sale did not go through,
and while the site was listed as a possible SuperFund site, funding
was then unavailable to begin cleanup.  This year, however, there is
active discussion on the possibility of its sale.  We have determined
that well 4 is now contaminated, and have drilled three additional
wells: 
\smallskip
\+ & well & distance & water table \cr
\+ & 5 & 1500 ft & 40 ft \cr
\+ & 6 & 1700 ft & 34 ft \cr
\+ & 7 & 1900 ft & 28 ft \cr
\smallskip
\noindent
We found contamination in wells 5 and 6, but not in well 7.

\bigbreak
\noindent
We need from your company:
\smallskip
{\rightskip\parindent
\item{1.} an analysis of the manner in which the contaminant has
spread from the site since the years in which the company was
operating, with some justification of your model, and 
\smallskip
\item{2.} a prediction of the amount of time it will take the water
contamination to reach a distance of 2500 feet from the lagoon (the
location of the nearest well providing drinking water).  Your
prediction should include an indication of the rate at which you
believe the contamination to be spreading and why.\par
}
\medskip
\noindent
To assure your success in the completion of this project, our
department's scientific expert, Dr.\ Gavin LaRose, will be available
to answer any technical questions you might have in the course of your
investigation---feel free to contact him (with all members of your
consulting team) with any questions you might have.  You should
additionally plan to see him by the 13th of this month with an
indication of your preliminary work on the project.  A further update
should be provided by the 25th, and your finished report is due by the
30th.  Failure to meet any of these deadlines will be grounds for
reducing your payment.

\bigskip
\noindent
We look forward to receiving your report, which should be typewritten
and 3--5 pages in length.  Equations explaining your solution should
be included in the report, and it is permissible to hand-write these
in blank lines between your typewritten explanation if this greatly
facilitates the production of the report.
\bigskip
\bigskip

\longindent
Sincerely,
\bigskip
\bigskip
\bigskip
\bigskip
\longindent
Jack C. Ousteaux\par
\longindent
Director, Lonlinc CPE

\bye