$(25\%)$ The mass $(m)$ of a radiactive element decreases with time $(t)$ according to the following equation:

$m=m_0-e^{0\mathrm{.}2t}$

Use the Newton$-$Raphson method to determine the time $(t)$ required for the mass $(m)$ to be $0$ kg if the initial

mass $(m_0)$ is $10$ kg $.$ Consider the initial estimate of $t=7\mathrm{.}5h.$ Show four iterations of the Newton$-$Raphson

method. Compute the absolute relative approximate percentage error $(|{}_a|)$ at the end of each iteration. Use

at least $4$ significant digits and rounding in all your calculations. Provide a plot of the equation, showing labels

and highlighting the solution of the equation. You are allowed to use MATLAB to create the plot.