$(8$ pts$.)$ A $4\mathrm{.}00cm10\mathrm{.}0cm$ rectangular copper loop with a total resistance of $2\mathrm{.}00m$ is placed in a uniform magnetic field such that its normal vector makes a $30\mathrm{.}0$ angle with the field direction as a function of time. If the strength of the magnetic field $($in Teslas$)$ changes with time $($in seconds$)$ according to

$B(t)=4\mathrm{.}00e^{1\mathrm{.}20t}-2\mathrm{.}00t$

Find the magnitude and direction of the current induced in the rectangle at $t=0\mathrm{.}5s.$