Tripling in 3,000 years (120-150 generations) is “exponential growth”? Sounds like a mighty small exponent, though technically true. 1.015 doubles every 50 years, so the use of “exponential growth” seems more for effect, than elucidation.
And, thankfully, they didn’t have an Endangered Species Act to worry about, otherwise the tree huggers would be whining about “saving, protecting, and reintroducing” sabre tooth cats and cave bears all over the place.
I’ve got a single mating pair of ancestors who lived over 500 years ago and appear to be the ancestors of most of the people in the United States. In short, yeah, that seems like a mighty low exponent.