\documentclass [12pt] {article}

\usepackage{graphicx, amsmath}

\topmargin 0pt
\advance \topmargin by -\headheight
\advance \topmargin by -\headsep
\textheight 8.9in
\oddsidemargin 0pt
\evensidemargin \oddsidemargin
\marginparwidth 0.5in
\textwidth 6.5in

\newenvironment{packed_itemize}{
\begin{itemize}
  \setlength{\itemsep}{1pt}
  \setlength{\parskip}{0pt}
  \setlength{\parsep}{0pt}
}{\end{itemize}}

\begin{document}
\begin{center}

\Huge{
Logarithms in Practice}
\end{center}

\noindent
While working in a group make sure you:
\begin{packed_itemize}
\item Expect to make mistakes but be sure to reflect/learn from them!
\item Are civil and are aware of your impact on others.
\item Assume and engage with the strongest argument while assuming best intent.
\end{packed_itemize}

\begin{enumerate}
\item How many years will it take \$5,500 to amount to \$8,000 if it is invested at an annual rate of 9\% compounded monthly?

\vspace{1.5in}

\item How many years will it take \$5,500 to amount to \$8,000 if it is invested at an annual rate of 9\% compounded continuously?
\vspace{1.5in} 

\item \emph{Exponential Growth Model}(\S3.1): A population that experiences exponential growth increases according to the model $Pe^{rt}$
where $P$ is the initial population, $r$ is the relative rate of growth, and $t$ is time.

Zombies! The population of zombies is 2 on Wednesday and 5 a day later.

\begin{enumerate}
\item If the population continues to grow exponentially, how many zombies will there be in a week?
\vspace{1.5in}
\item How long until the population of UW Tacoma is gone?\\ (note: UW Tacoma has about 5000 students)
\end{enumerate}


\newpage
\item \emph{Radioactive Decay Model:} If $P$ is the initial mass of a radioactive substance with a half life $h$, then the mass remaining $A$, at time $t$ is modeled by: 

$$A=Pe^{-rt}$$

\noindent where $r=\frac{\ln 2}{h}$.

A skeleton of a cat was found in a well and has a ratio of carbon 14 to carbon 12 that is 61\% of the corresponding ratio for living things.  (Carbon 14 is only make by living things, carbon 14 begins to decay to carbon 12 upon death.  The halflife of carbon 14 is 5730 years.)  About how long ago did the cat die?
 

%\vspace{-0.2in} \hspace{2.2in}\includegraphics[height=2.2in]{blank_5}


\vfill

\item \emph{Newton's Law of Cooling:} If $D$ is the initial temperature difference between an object and its surroundings, and if its surroundings have a temperature $T$, then the temperature of the object $A$ and time $t$ is modeled by:

$$A=T+De^{-kt}$$

\noindent where $k$ is a positive constant that depends on the type of object.


 Initially coffee has a temperature of $200^\circ$F in a room that is $70^\circ$.  After ten minutes the temperature is $150^\circ$.  What will the temperature of the coffee be after an additional ten minutes passes?


\vfill


\end{enumerate}



\end{document}