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 N become larger the further out we predict, because our fit gives an exponent with an uncertainty. Consider 2^{10 \pm 1}, this give a range of 2^9 \rightarrow 2^{11} or 512 \rightarrow 2048! 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 K which can roughly be thought of as K = E \cdot p where E is the number of people an average infected person comes into contact with and  p is the probability of transmission.


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Physics 132 Lab Manual by Brokk Toggerson and Aidan Philbin is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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