10. The figure 4 shows the curves \(\mathrm { f } ( x ) = A - B e ^ { - 0.5 x }\) and \(\mathrm { g } ( x ) = 26 + e ^ { 0.5 x }\)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{48f9a252-61a2-491d-94d0-8470aee96942-14_718_1152_347_340}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Given that \(\mathrm { f } ( x )\) passes through \(( 0,8 )\) and has an horizontal asymptote \(y = 48\)
a. Find the values of \(A\) and \(B\) for \(\mathrm { f } ( x )\)
(3)
b. State the range of \(\mathrm { g } ( x )\)
(1)
The curves \(\mathrm { f } ( x )\) and \(\mathrm { g } ( x )\) meet at the points \(C\) and \(D\)
c. Find the \(x\)-coordinates of the intersection points \(C\) and \(D\), in the form \(\ln k\), where \(k\) is an integer.