Eli5 Wtf is the difference between geometric growth and arithmetic growth
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Arithmetic growth: You start at some point (say 100) and then add 20 every day. So 100, 120, 140, 160, 180, 200… This is what happens if you have a jar of money and put a $20 bill in it every day.
Geometric growth: You multiply by 20%, and add that much, every day. So (with some rounding) 100, 120, 144, 172.8, 207.36, 248.832… This is what happens if you have a patch of bacteria in a lab dish where they get plenty of food.
You see, bacteria make baby bacteria, and then within hours those baby bacteria grow up and make more baby bacteria, so not only are you adding 20% every day, but the 20% you added yesterday is going to add even more today. So tomorrow’s count will be a bigger increase from today’s count, than today’s count was from yesterday’s count.
Geometric growth can add up *fast*. If you continue arithmetic growth for 90 days, you’ll have $1900 in the jar. If you continue growing the bacteria from the same 100 starting point, after 90 days you’ll have 1,337,556,524.
(Real world applications of geometric growth are often simplified cartoon stories that don’t take into account the real-world usually has limiting factors. If you calculate this bacteria geometric sequence for 2 years, it will predict you’ll have more bacteria than atoms on Earth, which is rather ridiculous. That’s because using a geometric sequence doesn’t account for when the bacteria reach the end of the dish, run out of food, choke themselves on waste products, and so on.)
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