Problem $2)$ Induced current in a square wire loop $[50$ points$]$

A square wire loop of side length $5$ cm has resistance $R=100$ and lies in the horizontal page plane. A uniform magnetic field vec$(B)$ is perpendicular to the page plane and pointing out of the page plane, and in $1\mathrm{.}0$ seconds it decreases linearly from $30$ mT to $10$ mT $.$

a$)$ Find the magnetic flux ${}_{B,i}$ through the loop at the beginning of the $1\mathrm{.}0-$s period.

b$)$ Find the magnetic flux ${}_{B,f}$ through the loop at the end of the $1\mathrm{.}0-$s period.

c$)$ Find the loop current I during the $1\mathrm{.}0-$s period.

d$)$ What is the direction of the loop current I $?$ Justify your answer.