3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9b0b8db0-79fd-4ad5-88c9-737447d9f894-10_541_618_248_671}
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\caption{Figure 2}
\end{figure}
The total mass of gold, \(G\) tonnes, extracted from a mine is modelled by the equation
$$G = 40 - 30 \mathrm { e } ^ { 1 - 0.05 t } \quad t \geqslant k \quad G \geqslant 0$$
where \(t\) is the number of years after 1st January 1800.
Figure 2 shows a sketch of \(G\) against \(t\).
Use the equation of the model to answer parts (a), (b) and (c).
- Find the value of \(k\).
- Hence find the year and month in which gold started being extracted from the mine.
- Find the total mass of gold extracted from the mine up to 1st January 1870.
There is a limit to the mass of gold that can be extracted from the mine.
- State the value of this limit.
M