$[$Secant Method $14$ pts$]$ The function $f(x)=e^x-x-2,$ has one root $$ in the domain $0,2.$

We want to find this root $$ using the secant method.

$($a$)$ Write a code that applies the secant method to $f$ in $0,2.$ Choose the code to stop when

the error $e_k=|f(x_k)|$ tol, where tol $={10}^{-8}.$ Choose the starting values $x_0=0\mathrm{.}5$ and

$x_1=1\mathrm{.}5.$ Display your code.

$($b$)$ Print out iterate value at each iteration and the order of convergence where available. Display

the output of your code.

$($c$)$ Knowing that the secant method, at best, is order $\frac{1+\sqrt[\phantom{2}]{5}}{2}$ accurate. Do your results

match this expectation?