Answer
(a) $\lim\limits_{t \to \infty}v(t) = v^*$
(b) $0.47~s$
Work Step by Step
(a) $\lim\limits_{t \to \infty}v(t)$
$=\lim\limits_{t \to \infty}v^*(1-e^{-gt/v^*})$
$=v^*(1-0)$
$= v^*$
(b) $v(t) = (1)(1-e^{-9.8~t})$
The terminal velocity is $1~m/s$
On the graph, we can see that the velocity reaches $0.99~m/s$ after $0.47~s$
