A lily pond doubles the number of lilies every month. One
day, you notice that 2% of the pond is covered. About how long will it be
before the pond is entirely covered?
Answer:
The doubling time is 1 month, so in two months the pond will be covered
to 8%, in four months to 32%, in five months to 64%. In six months this would
be 128%, i.e. more than is available. So it will take somewhere between five and six months.
To get the precise number, you must figure out how many doubling times it takes to
go from 2% to 100% coverage, i.e.
you have to solve the following equation for the doubling time x:
So, the pond will be
fully covered in 5.64 doubling times, i.e. 5.64 months from now.