Challenge #123: When will Rabbits Rule the World?

[JoeM]

This one has been on my whiteboard for awhile and I've been meaning to publish this challenge. This weekly challenge should be a fun one! The question we are trying to answer is: In what future month/year will a new breed of rabbits to exceed the human population 2:1?

Let's set some rules for how this new breed of rabbit populates so we can try to find the day our civilization will be be under the rule of our new-found long-eared overlords.

1) We will start with 1 female and 1 male rabbit born today (0 months old)
2) Each month, each female produces a litter of 4 bunnies: 1 male and 3 females
3) A female cannot start to reproduce until she has matured to 4 months of age
4) All rabbits live only to 24 months in age. (Alive months 0-23, they cease to live at the start of the 24th month)

5) Don't forget human population grows too! Assume a 0.058% month over month human population growth!

I have provided an answer, but there may be little monthly nuances that account for slightly different answers. Sound-off on when you found out it is going to happen!

[patrick_digan]

Spoiler

I went for an iterative macro. It only took 41 iterations.
Workflow:


Macro:

[TerryT]

I got the same month, but my numbers don't match exactly!

Spoiler

[CharlieS]

I got the same date, but slightly different population counts for humans and the Supreme Overlords. Maybe this is close enough to count like in horseshoes and Holy Hand Grenades.

Spoiler

785,514,304 long-eared overlords and 336,183,913 humans

[NicoleJohnson]

Slightly different human population for my final result, with 24 extra humans - which frankly, in this terrifying scenario, I will gladly take. 

Spoiler

Thanks for the super fun challenge, @JoeM! I can see why you were so excited for this one :) Now, off to go pull anything that looks like a carrot out of my garden, just in case...

Cheers,

NJ

[terry10]

Averting my eyes from the GIF, I didn't notice the 2:1 population threshold and spent way too much time trying to find the error in my workflow.  :(  

Spoiler

[mmongeon]

Here's my solution.

Like many of the other submissions, I don't have the exact same population numbers, but I end up on the same month.

Spoiler

Main workflow:

Iterative macro:

[patrick_digan]

@mmongeon Your solution truly made my day! 51 formulas in one formula tool! 

[Ladarthure]

Was very funny and made me learn how to use the iterative macro, thank's to @patrick_digan for the first answer and showing a way to do this macro (was planning to use multi_rows formula...

[ggruccio]

Going to see iterations of rabbits in my sleep!