%% Math 131, Fall, 2003
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,epic,eepic}

\pagestyle{empty}

\setlength{\textwidth}{6.5in}
\setlength{\oddsidemargin}{0in}
%% \setlength{\topmargin}{-.5in}
\setlength{\textheight}{9.25in}

\def\ds{\displaystyle}
\def\vp{$\vphantom{\big|}$}

\def\R{\textbf{R}}
\def\Item{\item{$\Box$}\quad}

\def\be{\begin{enumerate}}
\def\ee{\end{enumerate}}

\def\bd{\begin{description}}
\def\ed{\end{description}}

\def\Answer#1{$\phantom{.}$\hfill
        #1\quad\fbox{$\phantom{\Big|Answer}$}} 

\newcommand{\MyAnswer}[2]{$\phantom{.}$\hfill
        #1\quad\fbox{$\vphantom{\Big|}#2$}}

\newcommand{\clog}{\textrm{log}_{10}\,}

\newcommand{\soln}{\paragraph{Solution}}
\newcommand{\sep}{{\medskip\hrule\bigskip}}
\newcommand{\blank}{\underline{$\phantom{A blank}$}}

\begin{document}

\begin{center}
\textbf{Holy Cross College, Fall Semester, 2003} \\
\textbf{Math 131, Quiz \#3, Solutions}
Professor Hwang \\
\end{center}

\be
\item Each part of this question refers to the polynomial whose graph
  is shown below. Circle the correct answer or fill in the blank as
  appropriate.  You may assume that the graphing window is large
  enough to show global behavior.

  \bd
    \item{(a)} Does the polynomial have \textbf{even} or \textbf{odd}
      degree?

      \soln Odd degree (ends of graph head in opposite directions).
  
    \item{(b)} Is the leading coefficient \textbf{positive} or
      \textbf{negative}?

      \soln Negative (graph heads down as $x$~increases).
  
    \item{(c)} The smallest possible degree is~\blank.

      \soln Five (the graph has four bends).
  \ed

\begin{center}
\input{quiz03.eepic}
\end{center}

\sep

\item Let $L$~be the length of a mammal's femur, and let~$d$ be the
  diameter, both measured in inches. In this question, assume that the
  length and diameter are related by a power law $d = k\,L^p$.  Use
  the given data to estimate~$p$.
  \begin{center}
  \begin{tabular}{|c||c|c|}
    \hline
    \vp Animal:  & $d$:    & $L$: \\
    \hline
    \vp Squirrel & $0.06$ & $2$ \\
    \hline
    \vp Human    & $1.75$ & $20$ \\
    \hline
    \end{tabular}
  \end{center}
\vfil

\soln The length and diameter of the respective femurs give the
equations 
\[
0.06 = k\,2^p,\qquad 1.75 = k\,20^p.
\]
Dividing the second equation by the first,
\[
\frac{1.75}{0.06} = \frac{20^p}{2^p} = 10^p,\qquad
\text{or}\quad p=\clog\frac{1.75}{0.06}=\clog 29.1667\simeq\framebox{\vp1.465}
\]

\ee
\eject

\end{document}
