PS: Though it's not actually called exponential (as it isn't enr-3-month-periods but rather 2nr-3-month-periods ) but has a different name which I can't recall anymore.
If you've ever seen a growth chart, you know that newborns grow incredibly quickly, but the rate of growth tapers off over time. That being said, my daughter will be six feet tall by the time she's 2:
There's another problem that his math missed. His baby-making rate stands at one per three months. Extrapolating that for all humans puts the population's doubling rate at EVERY THREE MONTHS! In 10 years, there will be a lot of ~3 trillion kg kids!
If every 10 billion people can make a new earth every year, I think we should be able to get on top of this.
They're making the (possibly false) assumption that density will stay the same, so size must grow with weight.
Of course, it's equally likely that size will remain constant. It changes or it doesn't -> 50/50 odds. Until the point it all collapses into a black hole.