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Topic: Tricky logistic growth problem
Replies: 0

 Joshua Zucker Posts: 710 Registered: 12/4/04
Tricky logistic growth problem
Posted: Apr 27, 1998 9:28 PM

To follow up on Lou's solution, though, note that the relative growth
rate is slowing down from 17.5% to 15% during this time, so it should
be a bit more than 4.1 months.

Also the rule of 72 is pretty inaccurate for things as big as 15-20%.
It works much better around 6-9%, which, fortunately, mortgage rates
usually are.

For sufficiently small interest rates, like 1%, the rule of 69.3
becomes a much better approximation (since ln 2 is .693). But then we
make up for the fact that 72 is bigger than 69.3 by using ln (1+x) = x
which gives just the right balance for x's between .06 and .09.

For big numbers like 15% probably the rule of 75 is closer than 72.

My method was pretty similar to the E. Ghitelman's:
I found the inital growth rate at 4.375 rabbits/month
the final growth rate at 7.5,
took the average of those (rounding down, since I know it'll spend
more time near the lower growth rate) to get about 5.5+
and then 25 rabbits increase in population / 5.5+ rabbits/month average
growth rate gave me 4.5- months.

--Joshua Zucker