That is exactly the mistake climate folks make. You can’t extrapolate. As soon as the curve breaks it’s a different equation, a different model. You can only use interpolation equations safely within the data set. As soon as you go beyond what you know historically, it will diverge, unless you have a full cycle of data. You don’t have a full cycle for this virus and this population set. No one does. You think you have a good model because excel can fit a set of data to a curve? That is just incorrect.
The only thing I can give you is that there is a good chance that tomorrow will be close to today. But your second order fit only goes one direction - up. You will need a much more complex equation, probably something that includes sinusoidal terms as well as a polynomial, to fit to to all the data once this thing has actually gone full cycle. Then you have a model that might represent the future, assuming nothing changes. But things always change. So it’s still best guess.
I also see folks trying to compare cases per capita for different countries/states/counties - you’re not going to get anything usable because these areas are at different stages of progression - some countries even have different strains.
Actually, using Excel to fit curves was good enough to get my PhD and publish on my research. So I'm pretty comfortable with the program and the calculations. What I am looking for, actually, is any sign that the growth is slowing, which would be reflected in the graphs by a decreased R squared value on the trendline. At that point, it would be appropriate to start deriving the exponential equation for this disease--although I'm not going to do that, since I won't be publishing. As for the extrapolations, I am completely comfortable with making them, since, like any exponential growth function, the rate of growth follows a very predictable trajectory.
This is not even comparable to what the "climate folks" do. They have taken a faulty premise--that carbon dioxide's wide band of fluorescence in the infra red frequencies equates to an increase in the energy content of the atmosphere--and extrapolated all kinds of stuff from that. Garbage in, garbage out. The fields of microbiology, epidemiology, etc., have a LOT of data and research to validate the models regarding disease spread.
The only thing I can give you is that there is a good chance that tomorrow will be close to today. But your second order fit only goes one direction - up. You will need a much more complex equation, probably something that includes sinusoidal terms as well as a polynomial, to fit to to all the data once this thing has actually gone full cycle. Then you have a model that might represent the future, assuming nothing changes. But things always change. So it’s still best guess.
As I said above, I'm looking for a change in the R squared value, which could mean that the growth of cases is slowing. Sure, determining the actual exponential equation is a bit more complicated than using a polynomial (which I already know from a TON of experience is close to within a few thousands to the actual values calculated by an exponential equation). But it's not necessary, and I don't have the full data set in any case to determine the actual exponential equation. That's because I don't know and no one knows when the increase in new cases will slow.