> Just because the growth rate isn't constant, does not make it not exponential.
That's literally what makes it not exponential (I.e. when it falls low enough that it is no longer proportional to the derivative). Sigmoid functions, catenary functions (hyperbolic trig), even the complex exponential (regular trig), and the like all have exponential terms. We don't use the term "exponential growth" in any of these cases unless there is growth without bounds - aka the real coefficients are positive.
Human population is obviously not strictly exponential, as there have been worldwide phenomena that lower it globally, and these will happen again in the future, but if the net growth rate is even 0.1% it is not linear, it is exponential. Only when the growth rate equals the replacement rate (deaths) will it suddenly be static, but if it increases even a hair over that its exponential at that moment (because new humans produce more new humans).
Also as we know from microbiology human population with finite resources can't be exponential in the long run as resources will limit it, so sure its not an exponential function because it obviously is a logarithmic function (likely with a whole other side to the graph once it reaches its peak). Sure maybe we are smarter than this, but it does seem like a leap to get there. So yes technically you are 100% right human population is not and cannot be exponential, it just has been for the past few centuries, and there isn't a good reason to expect it not to be in the future.
That's literally what makes it not exponential (I.e. when it falls low enough that it is no longer proportional to the derivative). Sigmoid functions, catenary functions (hyperbolic trig), even the complex exponential (regular trig), and the like all have exponential terms. We don't use the term "exponential growth" in any of these cases unless there is growth without bounds - aka the real coefficients are positive.