Monday 8 August 2016

A maths problem

A very rare sort of alfalfa sprout is highly valued in the health food shops of the world. We discover that it grows wild on a remote, uninhabited Scottish island and set out to make lots of money. On our first visit we harvest one tonne. However the sprout population does not completely recover from harvesting and we soon discover that each harvest yields only 96% of the mass of the previous one, so that the second harvest gives us 0.96 tonnes, the third one 0.962 = 0.9216 tonnes, etc. Supposing we could go on indefinitely, what is the maximum total amount of sprout we could ever harvest from this island?