If we let the downward direction be the positive $x$ direction, then the equation of motion is
$\begin{align*}m \ddot x = m g - b \dot x\end{align*}$
With the initial condition that $\dot x (t = 0)$ , this differential equation can easily be solved for $\dot x$ :
$\begin{align*}\dot x = mg/b \left(1 - e^{-t b/m}\right)\end{align*}$
Thus, we can see that the answer (E) is correct.

Solution to 1996 Problem 31