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That first sentence could replace the entire paper. Growth functions are inherently/fundamentally exponential (regardless of whether we're talking about bacteri
by epgui 5y ago
That first sentence could replace the entire paper. Growth functions are inherently/fundamentally exponential (regardless of whether we're talking about bacterial colonies, populations of rabbits, compound interest or ROI), but the forces that act on the exponent change over time. It really is this simple.
- jasonwatkinspdx 5y agoOh, and what proof do you have to offer that those exponentials are not sigmoids?
- marginalia_nu 5y agoReal exponential growth is fairly rare outside mathematical models, it is almost always attenuated by logistical bottlenecks or resource scarcity after some initial phase.
- ravi-delia 5y agoThat's not really true though. Regardless of whether our growth is exponential or logistic, we haven't hit an inflection point yet. So if the past data is better fit by a linear function, the logistic nature of our growth can't be the reason.
- jacobolus 5y ago> Growth functions are inherently/fundamentally exponential but the forces that act on the exponent change over time By this standard, every function is “fundamentally exponential”. You can plot literally any (strictly positive, differentiable) function on a log scale and find the slope at every point. BAM! Look, an exponent (changing over time)!
- epgui 5y agoDon't be facetious. In real life, the forces acting on the exponent correspond to real things that are related to the thing we're observing grow. If you don't have a causal graph explaining why your exponent is changing, then your plot doesn't make sense.