\textbf{Part 1}

The table below shows the price of durum wheat in € per ton in the period
2016--2021.

{\begin{center}
\begin{tabularx}{.9\linewidth}{|l|l|*{6}{>{\centering \arraybackslash}X|}}\hline
\multicolumn{2}{|l|}{Year} & 2016 & 2017 & 2018 & 2019 & 2020 & 2021 \\ \hline
Years after 2016 & $x$     & $0$ & $1$ & $2$ & $3$ & $4$ & $5$ \\ \hline
\begin{tabular}[c]{@{}l@{}}Price of wheat\\(€ per ton)\end{tabular} & $y$     & $110$ & $140$ & $145$ & $170$ & $266$ & $341$ \\ \hline
\end{tabularx}
\end{center}}

\begin{enumerate}[a)]
    \item \nbPointsEnumi{2}\textbf{Draw} a scatter diagram to represent the data from the table.

    \item \nbPointsEnumi{1}\textbf{Determine} the average annual increase of the durum wheat price from
2016 to 2021.

    \item \nbPointsEnumi{4}\textbf{Determine} an equation in each of the forms $y = K \cdot A^x$ and $y = K \cdot \e^{a \cdot x}$
of the exponential regression of y on x using the data from the table.

Give the constants $A$ and $a$ correct to 3~decimals.
\end{enumerate}

In d) and e) use the exponential model $g(x) = 104 \cdot \e^{0.22x}$ for the price
in € per ton of durum wheat x years after 2016.

\begin{enumerate}[a)]
\setcounter{enumi}{3}
    \item \nbPointsEnumi{1}\textbf{Estimate} the price of durum wheat in € per ton in 2023.

    \item \nbPointsEnumi{2}\textbf{Compare} $g'(4)$ and $g'(5)$. \textbf{Explain} what these two values tell about
the wheat price.
\end{enumerate}

\medskip

\textbf{Part 2}

Two agricultural farms A and B produce wheat. Wheat harvests are
brought to a processing site which transforms the wheat into semolina
or flour and packs it into bags.

40\% of the wheat used at the processing site come from farm A, and
the rest comes from farm B.

45\% of the wheat from farm A is used to produce flour.

70\% of the wheat from farm B is used to produce semolina.

At the processing site a bag is selected at random.

\begin{enumerate}[a)]
\setcounter{enumi}{5}
    \item \nbPointsEnumi{2}\textbf{Calculate} the probability that the bag contains flour, and that the wheat
came from farm A.

    \item \nbPointsEnumi{3}Given the bag contains semolina,\textbf{calculate} the probability that the
wheat came from farm B.
\end{enumerate}

