A group of students are researching the rate at which ice thickens on a frozen pond. They have experimental evidence that when the air temperature is –T °C, the ice thickens at a rate T/14000x cm s^-1, where x cm is the thickness of the ice that has already formed.
On a particular winter day the air temperature is constant at –7 °C. At 12.00 noon the students note that the ice is 2 cm thick. Time t seconds later the thickness of the ice is x cm.
(a) Show that dx/dt = 1/2000x
(b) Solve the differential equation and hence find the time when the students predict the ice will be 3 cm thick.
Between me and my girlfriend we can't do it. And we're supposed to be clever. :S