(a)[2]
By sketching a suitable pair of graphs, show that the equation $2 + e^{-0.2x} = \ln(1 + x)$ has only one root.
(b)[2]
Show by calculation that this root lies between $7$ and $9$.
(c)[3]
Use the iterative formula $x_{n+1} = \exp\left(2 + e^{-0.2x_n}\right) - 1$ to determine the root correct to $2$ decimal places. Record each iteration to $4$ decimal places. [$\exp(x)$ is another notation for $e^x$.]