(i)[2]
By drawing a suitable pair of graphs, show that the equation $5e^{-x} = \sqrt{x}$ has one root.
(ii)[2]
Show that, if a sequence of values produced by the iterative formula $x_{n+1} = \frac{1}{2}\ln\left(\frac{25}{x_n}\right)$ converges, then its limit is the root of the equation in part (i).
(iii)[3]
Use this iterative formula, together with initial value $x_1 = 1$, to calculate the root correct to 2 decimal places. Show the result from each iteration to 4 decimal places.