My Daily Thoughts

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Exponential Growth

The greatest shortcoming of the human race is our inability to understand the exponential function.
Professor Albert Allen Bartlett's

One thing that COVID has taught us is another way of comprehending exponential growth.

Instead of a rate of return, there is the R0 value for COVID.

In Canada, the average R0 value has been around 2.  This means that on average, everyone who contracts COVID will infect 2 other people.  In investment terms, this is a 200% return.

Let’s say there is 1 person who is infected in a population.  For this thought experiment, we will assume that the people the person infects will be infected in a day. Therefore on day 2, two more people are infected bringing the total to 3.  On day 3 the 2 new people infect 2 people each plus the three bringing the total to 7. By day 10, 1023 people have been infected.  By day 19, 524,287 people are infected.  The next day 1,048575 people are infected.

See the table for all the numbers for the first 20 days.

Day New Cases Total Cases R0
1                           1.00                           1.00 2
2                           2.00                           3.00 2
3                           4.00                           7.00 2
4                           8.00                        15.00 2
5                        16.00                        31.00 2
6                        32.00                        63.00 2
7                        64.00                      127.00 2
8                      128.00                      255.00 2
9                      256.00                      511.00 2
10                      512.00                   1,023.00 2
11                   1,024.00                   2,047.00 2
12                   2,048.00                   4,095.00 2
13                   4,096.00                   8,191.00 2
14                   8,192.00                 16,383.00 2
15                 16,384.00                 32,767.00 2
16                 32,768.00                 65,535.00 2
17                 65,536.00              131,071.00 2
18              131,072.00              262,143.00 2
19              262,144.00              524,287.00 2
20              524,288.00           1,048,575.00 2

Luckily the Government has put restrictions in place to help keep these numbers in check.

Live the Adventure

Geoff

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