The model of continuous exponential decay never actually reaches $0$, however, in the real world, no quantity is truly continuous. It's made up of a large but finite number of discrete chunks (atoms/molecules/cents/what-have-you). Thus the continuous model necessarily approximate. Because such models are typically based on the behavior of random processes, when the actual number of chunks becomes small, the approximation is typically no longer a very good one, so the continuous model can't tell you precisely when you'll actually run out of "stuff".