%% Math 131, Fall, 2003
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\begin{document}

\begin{center}
\textbf{Holy Cross College, Fall Semester, 2003} \\
\textbf{Math 131, Answers to Review Sheet for Midterm 1}
Professor Hwang \\
\end{center}

\bd

\item{1a)}\quad $-16(2+h)$ feet per second

\item{1b)}\quad $-16(2t_0+h)$ feet per second

\item{1c)}\quad $-32t_0$ feet per second

\item{2)}\quad $2^{x+3}=8\cdot2^x$

\item{3)}\quad $\frac{1}{2}\sin 2x$

\item{4a)}\quad $V(t)=900(0.75)^t$ dollars

\item{4b)}\quad \$$878.68$; depreciates to nothing after about 42~months

\item{4c)}\quad \$$241.15$ per year; \$$208.85$ per year

\item{5)}\quad About $297$ feet

\item{6)}\quad Horizontal: $y=2$; Vertical: $x=-1$ and $x=\pm2$

\item{7)}\quad $f(x) = x^5+x-1$; $f(0)=-1<0$, $f(1)=1>0$.

\item{8)}\quad $x=\ln(y\pm\sqrt{y^2-1}) = \pm\ln(y-\sqrt{y^2-1})$

\item{9)}\quad Note that $(x-\sqrt{x^2-1})(x+\sqrt{x^2-1})=1$

\item{10a)}\quad $Q(t)=Q_0(0.9974266)^t$ (don't round off)

\item{10b)}\quad 269 years

\item{10c)}\quad $2.57672$\% per year

\item{10d)}\quad About $893.6$ years

\item{10e)}\quad $21518.74$ years, or about 80 half-lives.

\item{10f)}\quad No

\ed

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