\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus

Please login to create an exam or a quiz.

Algebra
Exponentials
New Random

A sample of 130 bacteria grows exponentially and increases by 28% each hour.

  1. How many bacteria will there be after 10 hours?
  2. How long does it take for the population to double?

  1. Using \(\displaystyle P=P_0e^{kt}\) gives \(\displaystyle P=130e^\frac{7 t}{25}\). Evaluating at \(\displaystyle t=10\) gives \(\displaystyle P=2138\) bacteria.
  2. The doubling time is \(\displaystyle t=\frac{\ln 2}{k}=2.48\) hours

Download \(\LaTeX\) 

\begin{question}A sample of 130 bacteria grows exponentially and increases by 28\% each hour.
\begin{enumerate}
    \item (10pts) How many bacteria will there be after 10 hours?
        \soln{9cm}{
            Using $P=P_0e^{kt}$ gives $P=130e^\frac{7 t}{25}$. Evaluating at $t=10$ gives $P=2138$ bacteria. 
        }
    \item (10pts) How long does it take for the population to double?
        \soln{9cm}{
            The doubling time is $t=\frac{\ln 2}{k}=2.48$ hours 
        }
\end{enumerate}
\end{question}

Download Question and Solution Environment\(\LaTeX\)
\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}
HTML for Canvas 
<p> <p>A sample of 130 bacteria grows exponentially and increases by 28&#37; each hour.
<ol type="a">
	<li>How many bacteria will there be after 10 hours?</li>
	<li>How long does it take for the population to double?</li>

</ol>
</p> </p>
HTML for Canvas
<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=130e^\frac{7 t}{25} " src="/equation_images/%20%5Cdisplaystyle%20P%3D130e%5E%5Cfrac%7B7%20t%7D%7B25%7D%20" alt="LaTeX:  \displaystyle P=130e^\frac{7 t}{25} " data-equation-content=" \displaystyle P=130e^\frac{7 t}{25} " /> . Evaluating at  <img class="equation_image" title=" \displaystyle t=10 " src="/equation_images/%20%5Cdisplaystyle%20t%3D10%20" alt="LaTeX:  \displaystyle t=10 " data-equation-content=" \displaystyle t=10 " />  gives  <img class="equation_image" title=" \displaystyle P=2138 " src="/equation_images/%20%5Cdisplaystyle%20P%3D2138%20" alt="LaTeX:  \displaystyle P=2138 " data-equation-content=" \displaystyle P=2138 " />  bacteria.</li>
	<li>The doubling time is  <img class="equation_image" title=" \displaystyle t=\frac{\ln 2}{k}=2.48 " src="/equation_images/%20%5Cdisplaystyle%20t%3D%5Cfrac%7B%5Cln%202%7D%7Bk%7D%3D2.48%20" alt="LaTeX:  \displaystyle t=\frac{\ln 2}{k}=2.48 " data-equation-content=" \displaystyle t=\frac{\ln 2}{k}=2.48 " />  hours</li>
</ol></p> </p>