## 26 March 2020

### Exponential growth - Year 10 maths revision

"When will I ever need to use logarithms, or raising something to the the power of 1/n in real life". During Covid-19, it turns out. Since no one likes logarithms, I thought I'd just post a few formulas. The following should work on any system of exponential growth.

(Naturally, for Excel formulas, substitute in the value or cell reference for X, Y, T, etc)

 Formula Excel Formula Example Initial Cases X 112 Aus # Mar10 Final Cases Y 2,431 Aus # Mar25 Time T 15 days Multiplier over duration M = Y/X =Y/X 21.71 Daily Multiplier MD = M1/T =(Y/X)^(1/T) 1.23 Daily % Increase =(MD -1) * 100 =((Y/X)^(1/T)-1) 22.8% Format as % Time to double T2X = loge2 / logeMD =LN(2)/LN((Y/X)^(1/T)) 3.38 days Time to 10x T10X = loge10 / logeMD =(Y/X)^(1/T)/LN(10) 11.22 days Convert from 'time to double' to 'time to 10x' T10X = T2X * loge10 / loge2 =TDOUBLE * LN(10)/LN(2) Convert from 'time to 10x' to 'time to double' T2X =T10X * loge2 / loge10 =TTEN * LN(2)/LN(10) Convert from 'time to double' to 'daily multiplier' MD = elog2 / T2X =EXP( LN(2) / TDOUBLE) Apply a daily multiplier for N days M = MDN =POWER(MD, NUMDAYS)