.01% improvements every second

If you make an improvement of 1% over 365 days you get:

>>> 1.01**365
37.78343433288728

If you take that improvement to be 0.01% instead over 365 days, you get:

>>> 1.0001**365
1.0371724113025478

I wanted to calculate what happens if you make 0.01% improvement every second, which is taking the same calculation and spanning it over the number of seconds in a year. I found it to be difficult.

>>> 1.0001**(365*24*60*60*60)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
OverflowError: (34, 'Result too large')

I figured Google could help me. But it gave me the answer I didn’t expect. But it makes sense.

Google told me it was infinity

Let’s proceed incrementally then. By day:

>>> 1.0001**(365*24)
2.401170202551435

By hour:

>>> 1.0001**(365*24*60)
6.689239090375805e+22

Wow! It’s already gigantic!

By minute:

>>> 1.0001**(365*24*60*60)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
OverflowError: (34, 'Result too large')

Okay, let’s see how Google does with it.

Nope. Google gives up.
No luck here too.

Okay. Now we’re getting somewhere thanks to Wolfram.

3.331218664514745224403075696142725612798196815923840… × 10^1369

Wow. I’m a total Wolfram fan for sure.

2.27085010951860670522948672484157641277497142226720… × 10^82171

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