Exponential growth is terrifying

This example illustrates just how fast exponential growth is. It was proposed on twitter by Charles Arthur (@charlesarthur) who attributes the idea to Simon Moores. The stadium version is a variant of the better known ‘grains of wheat (or rice) on a chessboard‘ problem. The stadium example is better, I think, because the time element gives it a sense of urgency, and that’s what we need right now. Here’s Wembley Stadium. The watering system develops a fault: in minute 1 one drop of water is released; minute 2, two drops, minute 3 four drops, and so on. Every minute the number of drops doubles. How long will it take to fill Wembley stadium? The answer is that after 44 minutes, before half-time, the stadium would overflow. Here’s why. The sequence is 1, 2, 4, 8, 16, . . . so the nth term in the sequence is 2n – 1. For example, the 4th term is 23 = 8. Next we need to know how many drops are needed to fill the stadium. Suppose a drop of water has a volume of 0.07 ml. This is 0.00000007, or 7 x 10-8, cubic metres. Wembley Stadium has a volume of 1.1 million cubic metres. So the stadium holds 15,714,285,714,285 drops. Or about 15.7×1012 drops. How many minutes does it take to get to this volume of water? After n minutes, the total volume of water will be the sum of all the drips up to that point. This turns out to be 2n-1. If this baffles you, check this video (in our case a =1 and r = 2). We want to solve for n, the number of steps (minutes...
Source: DC's goodscience - Category: Science Authors: Tags: corona COVID-19 epidemiology Uncategorized corona virus exponential geometric SARS-COV-2 Source Type: blogs