Answer
(a) $1.2$
(b) $0.56$
Work Step by Step
(a) With the given velocity equation, we can find the limit when $t\to\infty$ as:
$$\lim_{t\to\infty} 1.2(1-e^{-8.2t})=1.2-1.2\lim_{t\to\infty} (e^{-t})^{8.2}=1.2-1.2(0)^{8.2}=1.2$$
Thus the terminal velocity of the raindrop is $v(\infty)=1.2$ m/s
(b) See graph, a $99\%$ of the terminal velocity, we have $v(t)=0.99\times1.2=1.188$ and $t\approx0.56$ second
Note: the units are missing in the original problem.
