\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Suppose that $19911 is invested at an interest rate of 43% per year, compounded continuously. What is the account balance after 15 years?
Using \(\displaystyle P=P_0e^{kt}\) gives \(\displaystyle P=19911e^{\frac{43 t}{100}}\). Evaluating at \(\displaystyle t=15\) gives \(\displaystyle P=12597735\) dollars.
\begin{question}Suppose that \$19911 is invested at an interest rate of 43\% per year, compounded continuously. What is the account balance after 15 years?
\soln{4.5cm}{Using $P=P_0e^{kt}$ gives $P=19911e^{\frac{43 t}{100}}$. Evaluating at $t=15$ gives $P=12597735$ dollars.}
\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>Suppose that $19911 is invested at an interest rate of 43% per year, compounded continuously. What is the account balance after 15 years? </p> </p>
<p> <p>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=19911e^{\frac{43 t}{100}} " src="/equation_images/%20%5Cdisplaystyle%20P%3D19911e%5E%7B%5Cfrac%7B43%20t%7D%7B100%7D%7D%20" alt="LaTeX: \displaystyle P=19911e^{\frac{43 t}{100}} " data-equation-content=" \displaystyle P=19911e^{\frac{43 t}{100}} " /> . Evaluating at <img class="equation_image" title=" \displaystyle t=15 " src="/equation_images/%20%5Cdisplaystyle%20t%3D15%20" alt="LaTeX: \displaystyle t=15 " data-equation-content=" \displaystyle t=15 " /> gives <img class="equation_image" title=" \displaystyle P=12597735 " src="/equation_images/%20%5Cdisplaystyle%20P%3D12597735%20" alt="LaTeX: \displaystyle P=12597735 " data-equation-content=" \displaystyle P=12597735 " /> dollars.</p> </p>