% (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=blackletter
\font\sevenrm=cmr7
\def\longindent{\hskip 4in}
\def\logo{
%\rightskip 30pt
\vbox{\hrule\hbox{\vrule\kern
    5pt\vbox{\kern 3pt\noindent
{$\quad\circ\quad\circ\quad\circ$\hskip 3.5in\headerfont Medres,
Inc.\quad$\circ$\quad}

\par\kern 3pt}\kern
    -5pt\vrule}\hrule}
}
\def\caf{{\sl enieffac\/}}

\nopagenumbers

\centerline{\bf Math 105---Calculus I\quad Project 1}
\centerline{\bf a matter of alertness\dots }
\centerline{\sevenrm \copyright 1996 Gavin LaRose
(glarose@NebrWesleyan.edu), Nebraska Wesleyan University}
\centerline{\sevenrm permission granted to use and distribute for 
free in an academic setting.}
\bigskip
You are recently hired members of a successful independent
mathematical and scientific technical contracting company, and have
just been assigned your first contract.  The letter you received from
Medres, Inc., a medical research company said to have been recently
acquired by the world-wide MPC, Inc. conglomerate (the recently
expanded headquarters of which are to be found in the thriving
metropolis of Lonlinc, Skanebra), follows.

\vfill\eject

\logo
\medskip
\longindent Office 728 Ratherold Hall\par
\longindent 325 Eep Street\par
\longindent Lonlinc, SK\par
\longindent 04685\par
\medskip
\longindent 29 January, 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
Medres, Inc., always at the cutting edge of medical research, is
planning the announcement of a major breakthrough by its
pharmaceutical development division on the 14th of February.  We have
completed the manufacture and testing of a time-release capsule which
will consistently and safely release the proven stimulent \caf\ into
the taker's bloodstream over an eight-hour period, to produce
alertness and combat the effects of missed sleep.

\medskip
\noindent
Experimentally, we have observed that after taking one of our
capsules, the amount of \caf\ in the bloodstream is given by the
following data:
\smallskip
\settabs\+\quad& c(t) = \quad & 0.00 mg\quad & 0.00 mg\quad & 0.00
mg\quad & 0.00 mg\quad & 0.00 mg\quad & 0.00 mg\quad & 0.00 mg\quad &
0.00 mg\quad & 0.00 mg\quad\cr
\+& $t=$     & 0 hr    & .1 hr   & .5 hr   & 1 hr & 2 hr & 5 hr & 8
hr & 8.5 hr & 9 hr\cr
\+& $c(t) =$ & 2.01 mg & 1.58 mg & 1.06 mg & 1 mg & 1 mg & 1 mg & 1
mg & .02 mg & .01 mg\cr

\medskip
\noindent
In order to report completely on the drug, we need a function to model
this concentration data.  We have therefore contracted with your
company to develop such a model.  In addition, we also need to know,
based on the function you find, how long it takes for the initial
spike in \caf\ concentration to decrease to within .1 mg of its
long-term value. 

\medskip
\noindent
As our product announcement is scheduled for the 14th of February, it
is of utmost importance that we 
have your finished project report by the 12th of that month.  If
you have questions as you are working on the project, you should
confer with our chief consultant, Dr.\ Gavin 
LaRose, who has been instructed to assist you insofar as may be
possible (as he is currently under contract with the well-known
chemical reprocessing company Chemproc, Inc., he is unfortunately
unable to work full-time on this project---thus requiring our use of
your company).  Please also note that it 
is written into your contract that all members of your investigative
team who are working on the project 
contact him by the 5th of February to apprise
him of your progress on the project.  {\it Failure to do so will
result in a significant payment penalty.\/}  As is
usual, we have enclosed a copy of our technical report specifications,
which should govern the presentation of your results.
\bigskip
\bigskip
 
\longindent Yours sincerely,
\bigskip
\bigskip
\bigskip
\longindent Cever Etkoop, M.D.\par
\longindent President, Medres, Inc.
\bigskip
\bigskip
\noindent Encl: Technical report requirements

\vfill
\eject

\logo
\bigskip
\centerline{\bf Technical Report Requirements}
\bigskip
\noindent
\noindent 
All reports submitted to Medres, Inc. should be written so that 
all members of the board of directors can understand the issues raised
therein and therefore be able to appropriately use the report.  The
board members are all experts in various medical fields, but
unfortunately (though they all wish they had taken more) may only be
expected to have a background in precalculus mathematics.

\bigskip
\noindent Reports should further:
\bigskip
 
\item{$\bullet$} Be written in the first person plural (e.g., ``We
found the requisite data from the map\dots'').
\medskip
\item{$\bullet$} Include mathematical formulas in the the text of the
body of the report as appropriate to describe the methods and results
obtained.  (While the report must be typewritten, it is fine to neatly
hand-write formulas if that significantly simplifies its generation.)
\medskip
\item{$\bullet$} Clearly explain how the mathematical formulas that are
included bear on the problem being solved.
\medskip
\item{$\bullet$} Consist of
\smallskip
\itemitem{$\bullet$} An {\sl Introduction\/}, describing the problem
to be solved, and an indication of the mathematical method used to
solve it.
\smallskip
\itemitem{$\bullet$} A {\sl Body\/}, describing the mathematical
problem that was solved to answer the question(s) posed in the
introduction, and the solution to it.
\smallskip
\itemitem{$\bullet$} A {\sl Conclusion\/}, summarizing the results
obtained from the solution described in the body and clearly stating
their relevance to the original problem as described in the
introduction. 
\medskip
\item{$\bullet$} Be 2$1\over 2$--5 pages in length.
 

\bye
