One can use the relative change in a quantity to determine a rate of change such as ΔI/I=Qdt. When one does this with the CA Covid-19 data and a calculation based on the fit polynomial one gets a fairly good agreement on the results. X=K-K0 is the difference between the number of known cases and the value at which I=dK/dt peaks.
If we look at (K-K0)/I, the ratio of the cumulative number of known cases to it's daily rate of change, for the data we see that the average result is approximately one as expected.
The ratio calculated using the fit polynomial shows an apparent change in slope near X=0 which appears to be due to an error in the fit.
The fit of the polynomial to the data isn't perfect and its errors can show up in the plots of calculated results. Also the fluctuations in the observed values of K can show up in plots of results. Time delays in detection of infected individuals may also produce errors in the fit so one has to consider what's real and what's illusory.
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