Chapter 2.6, Problem 69E

In Chapter 9 we will be able 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.

(a) Find $\underset{t\to \infty }{\lim }v(t).$

(b) Graph v(t) if v* = 1 m/s and g = 9.8 m/s². How long does it take for the velocity of the raindrop to reach 99% of its terminal velocity?