A population of bacteria in a petri dish has a growth model given by the function

$$f(x) = 3^{x-4}$$

Where $x$ represents the number of days passed and $f(x)$ represents the \ul{number of thousands
of bacteria} present.

\begin{enumerate}
    \item \nbPointsEnumi{4}Using the grid below, draw a graph to represent the population of the bacteria over a
week long period. Use the following table of values if you wish.
\end{enumerate}

{\begin{center}
\begin{tabularx}{.95\linewidth}{|l|*{8}{>{\centering \arraybackslash}X|}} \hline
$x$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline
$f(x)$ & & & & & & & & \\ \hline
\end{tabularx}
\end{center}}

\begin{center}
\ifpdf
\includegraphics[width=8cm]{S6P3/2021_December/2021_12_S6P3_STRASBG_EN_BTest_ExoB3_IMG1.jpg}
\else
\psset{unit=1cm}
\def\xMin{0}
\def\xMax{7}
\def\yMin{0}
\def\yMax{10}
\begin{pspicture}(\xMin,\yMin)(\xMax,\yMax)
\psgrid[subgriddiv=5,gridwidth=.5pt,subgridwidth=.3pt,gridlabels=0pt]
\psaxes[linewidth=1.5pt,Dx=1,Dy=1]{->}(0,0)(\xMin,\yMin)(\xMax,\yMax)
\uput[ul](\xMax,0){x} \uput[dr](0,\yMax){y}
\end{pspicture}
\bigskip
\fi
\end{center}

\begin{enumerate}[resume]
    \item \nbPointsEnumi{2}Calculate the number of bacteria in the dish at the beginning of the observation.
    \item \nbPointsEnumi{2}Use your graph to estimate the amount of bacteria present on day 6.
    \item \nbPointsEnumi{2}Use your graph to estimate to the nearest day, how long it will take to pass 8000
bacteria.
\end{enumerate}
