It seems like the growth has two time scales (like an initial boundary layer, and a slower outer layer; sorry, too technical; the old math guy coming back to me). The most interesting graph is the one with multiple plateaus, indicating interesting dynamics going on.
You should have explained this more mathematically! "Exponential" may be a matter of measure theory. If you consider that all accounts start with one subscriber, than after a time period of n, the discrete measure of exponential must necessarily mean that a discrete interval can be found justifying exponential growth. For instance, if the number of subscribers is eventually 10, than a discrete exponential interval can be to fit the exponential function from 1 to 10. (And the worst case is 2, which is also exponential.)
The definition, however, that you're using is the mathematical definition: a derivative at any point of any exponential function is an exponential function. This fits the data. But it isn't necessarily what your friend meant!
Thanks for your suggestion, Adam. If you look at the bottom of the article (in the “disclaimers” section), I do point readers to what I mean by “exponential” - you can check out the link.
It seems like the growth has two time scales (like an initial boundary layer, and a slower outer layer; sorry, too technical; the old math guy coming back to me). The most interesting graph is the one with multiple plateaus, indicating interesting dynamics going on.
I'm guessing some mathematician has looked at this. Hoping people send me more data!
You should have explained this more mathematically! "Exponential" may be a matter of measure theory. If you consider that all accounts start with one subscriber, than after a time period of n, the discrete measure of exponential must necessarily mean that a discrete interval can be found justifying exponential growth. For instance, if the number of subscribers is eventually 10, than a discrete exponential interval can be to fit the exponential function from 1 to 10. (And the worst case is 2, which is also exponential.)
The definition, however, that you're using is the mathematical definition: a derivative at any point of any exponential function is an exponential function. This fits the data. But it isn't necessarily what your friend meant!
Thanks for your suggestion, Adam. If you look at the bottom of the article (in the “disclaimers” section), I do point readers to what I mean by “exponential” - you can check out the link.