After closing switch,
Capacitor is behave as short circuit element,
So,
I(to) = V/R
= 10/5
2
At t = infinite time capacitor is behave as open circuit,
I(t) = I(to)e^(-t/Ƭ)
Ƭ = time constant of circuit
Ƭ = R*C
= 200 μF
I(t) = 5*e^(-t/(500*10^(-6))
= 5*e^(-5000t) A
EXAMIANS