(a)[2]
By sketching an appropriate pair of graphs on the same diagram, show that the equation $e^{-\frac{1}{2}x} = x^5$ has exactly 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. Give the result of each iteration to 6 significant figures.