i. By sketching a suitable pair of graphs, show that the equation e^2x = 14 − x² has exactly two real roots.

ii. Show by calculation that the positive root lies between 1.2 and 1.3.

iii. Show that this root also satisfies the equation x = 1/2 In(14 - x²).

iv. Use an iteration process based on the equation in part iii, with a suitable starting value, to find the root correct to 2 decimal places. Give the result of each step of the process to 4 decimal places.