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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 1520%. It works much better around 69%, 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



