On Exponential Growth

fanaticflyer comments on Forgive me, but is the Singularity an event, or a process?: 
"Imagine a magic pipette. It is magic because every drop of water that comes out of it will double in size every minute. So the first minute there is one drop, the second minute there are two drops, the third minute four drops, the fourth minute eight drops and so on… This is an example of exponential growth. Now, imagine a normal sized football stadium. In this stadium you are sitting on the seat at the very top of the stadium, with the best overview of the whole stadium. To make things more interesting, imagine the stadium is completely water-tight and that you cannot move from your seat. The first drop from the magic pipette is dropped right in the middle of the field, at 12pm. Here’s the question: Remembering that this drop grows exponentially by doubling in size every minute, how much time do you have to free yourself from the seat and leave the stadium before the water reaches your seat at the very top? Think about it for a moment. Is it hours, days, weeks, months? The answer: You have exactly until 12:49pm. It takes this tiny magic drop less than 50 minutes to fill a whole football stadium with water. This is impressive! But it gets better: At what time do you think the football stadium is still 93% empty? Take a guess. The answer: At 12:45pm. So, you sit and watch the drop growing, and after 45 minutes all you see is the playing field covered with water. And then, within four more minutes, the water fills the whole stadium. This means that you think you are safe because it seems that you have plenty of time left, whereas due to the exponential growth you really have to take immediate action if you want to have any chance of getting out of this situation."