Consider the Newton$-$Raphson method to find a root of an equation. The error $E_i$ is defined as $(x_r-x_i)$ where $x_r$ is the real $($true$)$ solution. $E_0$ is the error of an initial solution $x_0.$ Answer following questions.

$($a$)$ How many iteration steps $(n)$ are required to reduce $E_n$ to an error threshold $($that is $($:$E_n$