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A sample of 800 bacteria grows exponentially and increases by 47% each hour.
\begin{question}A sample of 800 bacteria grows exponentially and increases by 47\% each hour. \begin{enumerate} \item (10pts) How many bacteria will there be after 33 hours? \soln{9cm}{ Using $P=P_0e^{kt}$ gives $P=800e^\frac{47 t}{100}$. Evaluating at $t=33$ gives $P=4355092677$ bacteria. } \item (10pts) How long does it take for the population to double? \soln{9cm}{ The doubling time is $t=\frac{\ln 2}{k}=1.47$ hours } \end{enumerate} \end{question}
\documentclass{article} \usepackage{tikz} \usepackage{amsmath} \usepackage[margin=2cm]{geometry} \usepackage{tcolorbox} \newcounter{ExamNumber} \newcounter{questioncount} \stepcounter{questioncount} \newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}} \renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}} \newif\ifShowSolution \newcommand{\soln}[2]{% \ifShowSolution% \noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else% \vspace{#1}% \fi% }% \newcommand{\hideifShowSolution}[1]{% \ifShowSolution% % \else% #1% \fi% }% \everymath{\displaystyle} \ShowSolutiontrue \begin{document}\begin{question}(10pts) The question goes here! \soln{9cm}{The solution goes here.} \end{question}\end{document}
<p> <p>A sample of 800 bacteria grows exponentially and increases by 47% each hour.
<ol type="a">
<li>How many bacteria will there be after 33 hours?</li>
<li>How long does it take for the population to double?</li>
</ol>
</p> </p>
<p> <p>
<ol type="a">
<li>Using <img class="equation_image" title=" \displaystyle P=P_0e^{kt} " src="/equation_images/%20%5Cdisplaystyle%20P%3DP_0e%5E%7Bkt%7D%20" alt="LaTeX: \displaystyle P=P_0e^{kt} " data-equation-content=" \displaystyle P=P_0e^{kt} " /> gives <img class="equation_image" title=" \displaystyle P=800e^\frac{47 t}{100} " src="/equation_images/%20%5Cdisplaystyle%20P%3D800e%5E%5Cfrac%7B47%20t%7D%7B100%7D%20" alt="LaTeX: \displaystyle P=800e^\frac{47 t}{100} " data-equation-content=" \displaystyle P=800e^\frac{47 t}{100} " /> . Evaluating at <img class="equation_image" title=" \displaystyle t=33 " src="/equation_images/%20%5Cdisplaystyle%20t%3D33%20" alt="LaTeX: \displaystyle t=33 " data-equation-content=" \displaystyle t=33 " /> gives <img class="equation_image" title=" \displaystyle P=4355092677 " src="/equation_images/%20%5Cdisplaystyle%20P%3D4355092677%20" alt="LaTeX: \displaystyle P=4355092677 " data-equation-content=" \displaystyle P=4355092677 " /> bacteria.</li>
<li>The doubling time is <img class="equation_image" title=" \displaystyle t=\frac{\ln 2}{k}=1.47 " src="/equation_images/%20%5Cdisplaystyle%20t%3D%5Cfrac%7B%5Cln%202%7D%7Bk%7D%3D1.47%20" alt="LaTeX: \displaystyle t=\frac{\ln 2}{k}=1.47 " data-equation-content=" \displaystyle t=\frac{\ln 2}{k}=1.47 " /> hours</li>
</ol></p> </p>