Can you predict how long a discontinuity will take to reach its target if it is low pass filtered at a certain frequency? Let's say you have a signal that relatively slowly rises from 0 to 1, then suddenly from one sample to the next drops back to 0, creating a sharp discontinuity. Let's say you run it through a one pole low pass filter at a given frequency, say 200 Hz to smooth it. 

Is there any way to predict or graph or calculate how long it will take after the discontinuity for the signal to reach 0 or near 0?
Infinitely long. It's an exponential decay, so it never goes back to 0. 

The time constant for a 200 Hz filter is $\frac{1}{2 \pi f} \approx 0.8ms $. About every 0.8ms it drops by about $2/3$ or every 1.84 ms it drops by a factor of 10.

If you define "almost zero" as one millionths you need to wait $6*1.8ms$ or about 11ms.