Earlier quoted context omitted.
Is it common for the cost per conversion curve to be a parabola?
Are you referring to the first graph in the post? If so, great question. I haven't looked into this much but wouldn't expect it to be parabolic - that was just an approximation to illustrate the points raised.
Alright, makes sense. I guess a parabola is the primordial (at least, to high school teachers) example so I understand why that is what you picked.
In terms of whether a parabola makes sense for the example, it's difficult for me to say. From my personal experience I would say this could maybe be done with differential equations and something akin to an R_0. Then you would also have steady states, but the advantage would be that you can actually see how your other parameters (coefficients in the differential equations) influence the conversion rate (in my analogy R_0).