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.
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), 2n = 1 + 15.7×1012. The easiest way to do this is to take the logarithm of both sides.
n log(2) = log(1 + 15.7×1012).
So
n = log(1 + 15.7×1012) / log(2) = 44.8 minutes
At the 43rd minute the stadium would be more than half full: (243 &...
Source: DC's goodscience - Category: Science Authors: David Colquhoun Tags: COVID-19 epidemiology Uncategorized exponential geometric Source Type: blogs
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