(i) By sketching a suitable pair of graphs, show that the equation \(5e^{-x} = \sqrt{x}\) has one root.

(ii) Show that, if a sequence of values given by the iterative formula \(x_{n+1} = \frac{1}{2} \ln\left(\frac{25}{x_n}\right)\) converges, then it converges to the root of the equation in part (i).

(iii) Use this iterative formula, with initial value \(x_1 = 1\), to calculate the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.