I'd chose a logistic-like curve to fit (since extrapolating to infinite population the ratio should approach 1 and 0 population it should approach 0).

I'm actually wondering if the model was fixed to have an intercept at (0, 0). That line looks way off.

I wonder at the same thing. Allow the intercept to change and you'll get a massively better predictor. That will also stop moderately higher density counties from being green, and moderately lower density ones from being pink.