\documentstyle[12pt,twoside,amstex,amsfonts,psfig]{article}

\raggedbottom

\input{macros-course}

\newtheorem{falsethm}[theorem]{False Theorem}

\begin{document}

\tutprobn{5}{3/5/99}{March 5, 1999}


\section{Team Problems}

\begin{problems}

\problem Is a Harvard degree really worth more than an MIT degree?!  Let
us say that a person with a Harvard degree starts with \$40,000 and gets a
\$20,000 raise every year after graduation, whereas a person with an MIT
degree starts with \$30,000, but gets a 20\% raise every year.  Assume
inflation is a fixed $8\%$ every year.  That is, \$1.08 a year from now is
worth \$1.00 today.

\bparts

\ppart How much is a Harvard degree worth today if the holder will work
for $n$ years following graduation?

\ppart How much is an MIT degree worth in this case?

\ppart If you plan to retire after twenty years, which degree would
be worth more?

\eparts

\problem We begin with two large glasses.  The first glass contains a pint
of water, and the second contains a pint of wine.  We pour some fixed
fraction, $f$, of a pint from the first glass into the second, stir up
the wine/water mixture in the second glass, and then pour the same
amount $f$ of the mix back into the first glass.  We now repeat this
pouring back-and-forth process a total of $n$ times.

\bparts

\ppart
Describe a closed form formula for the amount of wine in the first glass
after $n$ back-and-forth pourings.

\ppart
What is the limit of the amount of wine in each glass as $n$ approaches infinity?

\eparts

\end{problems}
\end{document}

