How many years does it take to double something?
If a variable is growing at r% per annum, the number of years it takes for it to double is the logarithm of 2 in the base 1+r... but in a surprising mental math helper, y=log(2,1+r) is very well approximated by y=70/r. This result is surprising stable for large ranges of r, say 1% to 200%.
So, if the population of a country grows at 1% p.a., it takes 70 years to double, if it grows at 5% p.a., it only takes 14 years!
The approximation error (actual minus estimate) is also relatively stable at 0.25 to 0.3 years (3 to 4 months) for r>5%. So, to look cool, mention that "if sales keep increasing at 23% per annum, it will take 3 years and 4 months for this company to double its size"!
So, if the population of a country grows at 1% p.a., it takes 70 years to double, if it grows at 5% p.a., it only takes 14 years!
The approximation error (actual minus estimate) is also relatively stable at 0.25 to 0.3 years (3 to 4 months) for r>5%. So, to look cool, mention that "if sales keep increasing at 23% per annum, it will take 3 years and 4 months for this company to double its size"!
posted by DS at 3:05 PM
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