I was going to call this ‘the exponential function’, but I didn’t want to put you off.
This is a key force behind much of Anything Yet: if things grow steadily (say, at the rate of few percent per year) and continue to grow at that rate, it doesn’t take long for that growth to become enormous – we might say overwhelming, and we should also say all-consuming.
The classic line about this is from Dr Albert Bartlett, Manhattan Project alumni and all-round interesting guy:
The greatest shortcoming of the human race is our inability to understand the exponential function.
I’m not sure I’d go as far as that, but he makes an important point. Here are a couple of great introductions to the idea.
The first is from Chris Martenson’s Crash Course:
I might come back to The Crash Course – the Incidental Economist a review expressing some caveats I have about it here.
The second is Albert Bartlett himself with a more involved but really helpful explanation: