2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c8b85e00-4549-4219-a75d-85f67ccb8e16-2_638_675_644_445}
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\caption{Figure 1}
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Figure 1 shows the curves \(y = 3 + 2 \mathrm { e } ^ { x }\) and \(y = \mathrm { e } ^ { x + 2 }\) which cross the \(y\)-axis at the points \(A\) and \(B\) respectively.
- Find the exact length \(A B\).
The two curves intersect at the point \(C\).
- Find an expression for the \(x\)-coordinate of \(C\) and show that the \(y\)-coordinate of \(C\) is \(\frac { 3 \mathrm { e } ^ { 2 } } { \mathrm { e } ^ { 2 } - 2 }\).