If every woman has 15 kids (*edit, Doh! 16*), and everyone dies at age 100?

1:53 PM 5/6/11

ASSUMPTIONS:

1. Every woman has 15, and only 15, kids. (*Change to 16. Half male, half female. Note that in real world, it's about 105 males / 100 females. I'll work the bugs out later.*)
2. Everyone dies at exactly age 100, no sooner and no later. Nobody dies in an accident, or for any reason at all, earlier than at age 100.
3. There are no technological advances that make us live longer than 100, or that enable us to have more than 15 kids.

At what point (if any) is the number of people dying at age 100 equal to the number of people being born?

We are not like bacteria. Bacteria reproduce infinitely. But humans can only have a limited number of offspring in their entire lives. There is a little bit of flexibility on that limit - menopause might come later, births might come at an earlier age, there might be less time in between children - but there is a maximum number somewhere.

One bacterium can reproduce over and over again, infinitely, forever. All of its children can also reproduce infinitely forever. They just break in half or something. Then the halves break in half.

They don't really 'die,' do they? Or do bacteria have a programmed death time too? They might, actually. I'd have to read about it. In fact, I remember this from reading about the study of aging: there is such a thing as programmed cell death.

But I'm not worried about the bacteria and whether or not they have a programmed time of death. I'm just saying that each woman can only have a maximum number of kids.

This is a mathematical formula. I need to put it on a graph so I can see it, and I don't have time to do it now.

Is there, or is there not, some maximum number of humans who can be born, while the 100-year-olds die off as quickly as new people are born? It's been so long since I did algebra that I'm not sure how to phrase this as an algebraic formula (though I might if I had more time).

I'm picturing a 'demographic surge' where the number of people TEMPORARILY increases a lot, and then stabilizes, simply because we cannot add any more people faster than they are dying off at age 100. But I need to prove it mathematically to make sure. The temporary demographic surge is a time period where it LOOKS as though we are having 'exponential growth.'

I need to verify this - I could be totally wrong about this. I wish I had time right now while it's fresh in my mind.

By the way, this doesn't even apply to the real world. It is totally abstract and the real world functions in a completely different way. However, I'm approaching this at the mathematical level for the sake of argument. I just can't use my mind to create mental images the way I used to before I was being attacked. If I were able to visualize it in my mind, I'd already know the answer without having to make a graph. I'd already know whether or not it was possible, or impossible, to reach some number where the 100-year-olds were dying at exactly the same speed as the new people were being born. It's very frustrating not to be able to think without being attacked and interrupted. I should already know this.

Remember, no woman can have more than 15 kids. There are 15, and only 15, and it stops, forever. (Again, don't take that literally. In the real world it varies.) (*edit, 16 kids*)