Expert: Paul Klarreich - 5/29/2006

Question
I create stories, and this came up in one of my story lines, so it's just a personal situation.

Math Problem:  Due to his unique ability to absorb sustenance, a metamorph can supply 200 pints of blood, per day.   It takes 4 pints to cure a Shoshondrea of an otherwise fatal disease (so 50 immediate cures / day).  After 2 weeks, the blood supplied by the metamorph will have overtaken the Shoshondrea’s own blood, and the Shoshondrea will be able to supply a pint of blood, each week, to add to the supply provided by the metamorph. There are 3 billion Shoshondrea.

How long will it take to cure all the Shoshondrea?

I don't know how to set up an equation like this,
Gail


Answer
Hi, Gail,

It would take too long to completely work this out, but since the S will each propagate a cure at a rate proportional to the number present, you have a situation similar to the Fibonacci sequence.

Leaving aside the contribution of the M, you have 50 S who can now cure 12.5 others.  So the number increases proportionally to the number already cured, having elements of an exponential function as well.

If it's really important, let me know.

Paul