$(20$ points$)$ For the circuit below the switch is opened at time $t=0.$ Assume steady$-$state conditions for $t<mn>0</mn>$

a$.(10$ points$)$ Determine $i_0(t)$ for $t>0.$

b$.(5$ points$)$ Sketch $i_0(t)$ for $8t=0\mathrm{.}50$ seconds

$c.(5$points$)$ What $is$ the current through the $8$ resistor $att=0\mathrm{.}5$ seconds?