Understanding Exponential Growth
When you try to predict the future with an exponential growth model which includes uncertainties, the uncertainty in your prediction grows exceedingly quickly the further out you predict. . The uncertainties in the number of cases become larger the further out we predict, because our fit gives an exponent with an uncertainty. Consider , this give a range of or ! A small difference in the exponent has a huge impact in the number.
However, this small change in exponent yielding large changes in result can be used beneficially. The fit, in our case, yields the constant which can roughly be thought of as where is the number of people an average infected person comes into contact with and is the probability of transmission.