(i) By sketching a suitable pair of graphs, show that the equation \(\ln(x+2) = 4e^{-x}\) has exactly one real root.

(ii) Show by calculation that this root lies between \(x = 1\) and \(x = 1.5\).

(iii) Use the iterative formula \(x_{n+1} = \ln\left( \frac{4}{\ln(x_n + 2)} \right)\) to determine the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.