Help with the Automatic Baby Cannon

Okay... this isn't what it originaly sounds like.

https://www.imzy.com/worldbuilding/post/almost_hilarious_poplulation_growth/comment/f21a14c0-bd8c-11e6-9b8e-25c1d4d83c2e?_notif=14bfd8f6-be2e-11e6-a436-b5ad269b1a02

I came here from the wroldbuilding community after we seemed to be trying to do a job that we seem to be horrible at and this community seems like there might be some people that understand how to do "a simple mathematics"

I'm trying to do a story which contains a society which is pushing the human reproductive system to the absolute limit (hence the joke in the title), trying to go from 10-20 thousand people to a population of five billion in less than a century. The only problem is that we're not really sure how to calculate it.

Can anyone here give me an equation to figure this out, the maximum growth rate for a population of humans or estamate for what would be the minimum starting population to get from one to the other within the century time limit that the story requires (though I can push a few of the variables... to a point)

Thanks, and happy mathing.