I think the problem lies with your model/question. You’re taking it for granted that the math is 2^n , because that works for a couple generations at a time that a human can hold in their brain at once. I think that’s leading you astray. The concept of “generations” is also tenuous and mostly only works for a limited number of generations of specific individual ancestors of one specific single organism you’re looking at. As boomer/millennial discourse has proven, generations are not actually, like, a thing, they’re just these constructs we use to explain things. What makes sense to describe a 30yr period in your own life as you relate to your parents and children does not work very well for describing a 300yr period where the timing of births is all over the place.

When you compare two separate peoples’ family trees, they don’t align neatly, you just get a forest. It’s not like the human population just iterates forwards as a group every so many ticks like in Conway’s Game of Life.

You can perform this simple check on your model: If the population has grown, that means at any instant, the “moment of birth rate”, if you will, will on average be positive. There are more babies being born than people dying. How then can the number get larger as you go back? There were always fewer people each year back. We know that because there are always more people each year forward.