agreed ... your blog post tried to convey a very simple and punchy idea, and you didn't make any pretenses about it being 'mathematically accurate' or whatever, so i'm astounded that people have nitpicked on your curves not being accurate or whatever.
a piece of presentation advice i've heard for creating graphs and diagrams is that if you don't want people to nitpick on details, make a really crappy low-fidelity sketch so that people don't have an expectation of precision. i once got ripped on because i drew a line that looks like 1 / x^2 to talk about inverse correlation, but people nitpicked on whether it was a power law, 1/x, whether the integral converges, etc., which was totally irrelevant to my argument. if i had made a crappy hand-sketch on the board, then people might not have been as critical
And don't include mathematical equations. They are meant to be precise.
A closer analogy might have been with growth of a bacteria colony: It's more or less exponential and you have to keep the right conditions up --- even in the beginning where you do not see anything, yet.
a piece of presentation advice i've heard for creating graphs and diagrams is that if you don't want people to nitpick on details, make a really crappy low-fidelity sketch so that people don't have an expectation of precision. i once got ripped on because i drew a line that looks like 1 / x^2 to talk about inverse correlation, but people nitpicked on whether it was a power law, 1/x, whether the integral converges, etc., which was totally irrelevant to my argument. if i had made a crappy hand-sketch on the board, then people might not have been as critical