The story of the frogs
This is a simulation of exponential growth as set out by Dennis Sherwood in his book, Seeing the Forest for the Trees: A manager's guide to applying systems thinking.  The story of the frogs is this:

A colony of frogs is living happily on one side of a large pond.  At the other side of the pond is a lily pad.  One day, a chemical pollutant flows into the pond, which has the effect of stimulating the growth of the lily pad so that it doubles every 24 hours.  This is a problem for the frogs, for if the lily pad were to cover the pond entirely, the frog colony would be wiped out.

Q1: how would you describe the growth of the lily pad?
Q2: if the lily-pad can cover the entire pond in 50 days, on what day is the pond half covered?
Q3: The frogs have a method of stopping the growth of the lily-pad, but it takes them 10 days to put their method into effect.  What proportion of the pond is covered at the latest possible time the frogs can take action to save themselves?

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