(a)[2]
Sketch a suitable pair of graphs on the same diagram to show that the equation $e^{-\frac{1}{2}x} = x^5$ has only one real root.
(b)[3]
Use the iterative formula $x_{n+1} = \sqrt[5]{e^{-\frac{1}{2}x_n}}$ to find the root correct to $4$ significant figures. State the result of each iteration to $6$ significant figures.