An exponential growth graph looks like the following. (I generated this graph simply by starting with the number 1, and then doubling it 37 times.)
It looks like the line of growth goes "on and on" for quite a while until it "takes off" at about doubling 31, where it simply accelerates into the stratosphere. This has been called the "long tail" or the exponential growth curve. It looks like it's flat until it accelerates: so it's "hard to know" until it takes off.
Of course, this isn't quite the reality. The line from 0 to 31 is only flat relative to the enormous doubling growth about to happen after line 31. In other words, there is growth from points 0 to 31, but that growth is miniscule compared to the doubling that takes place between 36 and 37.
If we "back up" in the sequence, we can see pre-31 growth is clearly obvious:
This again looks like the exponential curve taking off. It's the same thing, all over again: but note the point between 29 and 30, which has the characteristic "hockey stick" exponential growth, looks like a "small" curve on the previous slide.
Let's back it up to iteration 20, and see the same thing:
And then, once more, to iteration 10:
Exponential growth isn't something that takes a long time to see. You don't have to wait 30 weeks (or 30 months) and then suddenly it takes off. If you know what to watch for, you will see it early--as early as iteration 4 (whether that's hours, weeks or months). Doubling isn't magic or faddish: it's a repeatable system. And if you aren't seeing doubling early you won't see it later on either.
If your processes aren't yielding doubling, it's time to review them. If you can't measure doubling, it's time to institute measurement systems that can.