It is possible to show, under certain assumptions, that the velocity $v(t)$ of a falling raindrop at time $t$ is $v(t)=v^*(1-e^{-gt/v^*})$, where $g$ is the acceleration due to gravity and $v^*$ is the terminal velocity of the raindrop.

Suppose $v^*=1 \;m/s$ and $g=9.8\; m/s^2$.
(a) Find $\displaystyle \lim_{t \to \infty} v(t)$.
(b) How long does it take for the velocity of the raindrop to reach 99% of its terminal velocity? Round your answer to the nearest hundredth.

(a) m/s
(b) s