Terminal speed with linear drag

[PsychonautQQ]

Homework Statement

An object moves through a liquid horizontally against a linear drag force given by F = -cv
What is the terminal velocity? Initial Velocity is V_0

Homework Equations

F=ma

The Attempt at a Solution

m(dv/dt) = -cv
-->
(dv/v) = (-c/m)dt
ln(vf/v0) = -ct/m
vf=v0*e^(-ct/m)
which says that as time goes to infinity that vf will equal v0 but that doesn't make any sense physically... what did I do wrong here?

 

[vela]

Take the limit incorrectly? $V_f$ approaches 0 as $t \to \infty$, no?