While I can't exactly anticipate the precise nature of your "math," let me try in a way to say what the mainstream understanding is. The original insight came from Malthus, who influenced young Darwin.
Which is to say that Paleolithic hunter-gatherer technology allows a certain population density, a pretty thin one. Add a certain amount of farming and you can have some cities and an overall greater population per square mile.
At any given technological level, there's a competition for resources and a ceiling on population growth.
Having once reached the Malthusian limit, it takes improvements in technology to increase food production to allow population growth. For most of human history we were low-tech and basically just another animal species competing with the rest.
I'd pretty much guarantee up front that any model your "math" represents doesn't consider any of that. Thus, it's hardly worth doing any arithmetic. If the model is bad, the scenario is "Garbage in, garbage out."
Something tells me you shouldn't hold your breath waiting to see your interlocutor post the Lotka-Volterra equation.
;-)