Your a PhD in I don’t know what so I cant tell you anything i guess. You clearly weren’t a PhD in math or engineering. Only the start of the cycle could be described as close to an exponential curve. The growth AND decay of the cycle is not an exponential, it going to be more sinusoidal, which is described by Fourier better than polynomial.
It is obvious that you do not have a PhD in a life science, nor do you have ANY experience modeling growth curves. You should expect that someone who has a PhD in a life science is intimately familiar with the mathematical and statistical functions necessary for data analysis in that field.
When I use a polynomial to fit the curve, it is because I know, with 20 years experience, that the polynomial is accurate to within a few thousandths, or to within 0.0000n of the actual value. In other words, the error is so low that it is swallowed by background noise.
Don't make the mistake of thinking that because you studied engineering, that you have any kind of understanding of the life sciences or the mathematics that we use.
just because you have a PhD doesn’t mean you can’t learn something new. If you don’t believe that you’re not so bright.
I simply cautioned you about extrapolating on data. Then you threw the PhD card. Kind of like liberals throwing the race card. You know more than me, or so you imagine. Like I said, carry on PhD.
PS - R-squared, the square of the fit residuals, will grow, not decrease, once your curve breaks. That’s when your poly breaks down. The poly trajectory is less steep than the exponential trajectory, so when it breaks to fewer cases, going exponential is the wrong direction. You don’t even understand the basic math behind the excel formulas. A common mistake for most people who become excel experts, but for a studied PhD, a sign of over confidence or a failing education system.
You're using it all wrongly...not you're fault though, as you've been brainwashed to stay within the lines. I've seen many brilliant people absolutely terrified to even consider anything outside of what some AH of a professor drilled into their skulls - the professors themselves suffering from the same institutional paranoia.