(a)[2]
On one set of axes, sketch the graphs of $y = 1 + e^{2x}$ and $y = |x - 4|$.
(b)[2]
Let the graphs intersect at the point $P$. Show that the $x$-coordinate of $P$ is given by the equation $x = \frac{1}{2}\ln(3 - x)$.
(c)[3]
Use an iterative method based on the equation from part (b) to determine the $x$-coordinate of $P$ correct to 3 significant figures. Start from $0.45$ and write each iterative value to 5 significant figures.