his graph illustrates the
derivation of an entry in the SelfReference
Collection...
An
enterprise growing at the rate of
exactly 17.65717% per year will become
exactly 17.65717 times larger in
exactly...
17 years, seven months, 29
days, and 21 hours
...which is
exactly 17.65717 years.

...and sophisticated
solvers will recall that the equation S
= (1+ i /100)^{n}
applies, which most often makes the relationship
among the variables irrational even for integer
values of S, i,
and n. Such is the
inconvenience of 'exponentials' as was seen by
solvers of Rational Roots.
DoublingTime applies a most
convenient formula n = 72 / i,
which is
well known to economists
and futurists
who need to make comparisons involving
growth rates.
 The formula n = 72 / i
answers the question, How many growth
intervals n (in years or
months) are required for an
'enterprise' (or volume or budget or
demand or pollution or...) that is
growing at a given rate i %
per growth interval to double in size S
= 2?
 The formula can be
turned around the other way: i
= 72 / n to answer the
question, How fast does an enterprise
need to grow (i %) to
double its size in n
growth intervals?
Inasmuch as 72 is divisible by
10 integers (2, 3, 4, 6, 8, 9, 12, 18, 24,
36), the formula seldom needs a
calculator. However, as solvers of Easy as Pi know,
such an approximation is not perfect.
