6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{57ea7a94-6939-4c12-a6fd-01cd6af73310-10_1004_1120_260_420}
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\caption{Figure 1}
\end{figure}
Figure 1 is a sketch showing part of the curve with equation \(y = 2 ^ { x + 1 } - 3\) and part of the line with equation \(y = 17 - x\).
The curve and the line intersect at the point \(A\).
- Show that the \(x\) coordinate of \(A\) satisfies the equation
$$x = \frac { \ln ( 20 - x ) } { \ln 2 } - 1$$
- Use the iterative formula
$$x _ { n + 1 } = \frac { \ln \left( 20 - x _ { n } \right) } { \ln 2 } - 1 , \quad x _ { 0 } = 3$$
to calculate the values of \(x _ { 1 } , x _ { 2 }\) and \(x _ { 3 }\), giving your answers to 3 decimal places.
- Use your answer to part (b) to deduce the coordinates of the point \(A\), giving your answers to one decimal place.