One Percent

Growth fascinates me, as a lot of you know. Growth rates fascinate me, too, and since this hasn't really been discussed here yet as far as I can tell, I thought it might be a good illustration of how quickly exponential growth can get out of hand.

Suppose someone...oh, let's say me...started at a height of 5 feet and grew just 1% taller with each passing minute. What would happen if I could keep that up for a whole week?

If you measure me after just a minute, I've only grown 1% taller, which works out to a little over half an inch. How cute! You probably couldn't even tell I was getting bigger. But that growth starts compounding, just like the interest on your debt...

In ten minutes, I'm just over 5' 6". In a half an hour, I'm just shy of 6' 9". Come back after a whole hour has passed, and I'm pushing 9' 1". A whole hour, and I haven't even hit 10 feet yet!

Come back after an 8-hour shift at work, and you'll find a building-sized Mataki, nearly 600 feet tall. Somewhere between 11 and 12 hours, I'll hit the mile-high mark.

Now it gets scary. You might want to catch a flight somewhere far away, have a good night on the town, and try to get some rest. When you wake up, turn on your TV 24 hours after all this started, and I'm sure to be the news...all 1600 miles of me. I'd be sprawling across a good half of the country. I'd be earth-sized almost three hours later.

Let another day go by, 48 hours total, and I'll be 2.64x10⁹ miles tall...I'd stretch from the sun to Neptune...almost as big as the diameter of the solar system.

About halfway through the third day, at 61 hours, I'd be a light-year tall.

Twenty hours later, during the fourth day and a little over 80 hours after all this started, I'd be as big as the Milky Way. Just six hours later, I'd be bigger than the Local Group, our neighborhood of galaxies.

If you consider the universe to be 15 billion light-years across, I'd reach that height in just over 100 hours on the fifth day.

And I still have almost two more days to grow.

I'd end up about 3 sextillion (3,000,000,000,000,000,000,000) times larger than the current theorized universe by the end of the seventh day.

All that from 1% growth per minute. These ridiculously but delightfully large numbers are why exponential functions usually don't continue very long in nature, and why credit card debt can really pile up if you don't take care of it.

Good old S=S₀(1+r)^t.