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)