Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
We know that the current is given by
$$I=\dfrac{dQ}{dt}$$
where $Q=20(1-e^{-t/2})$, so
$$I=\dfrac{d }{dt}\left[20(1-e^{-t/2})\right]$$
$$I=20 \left[ -\frac{-1}{2}e^{-t/2} \right]$$
$$\boxed{I= 10e^{-t/2}}$$
$$\color{blue}{\bf [b]}$$
See the graph below,