Water flows out of a tank through a hole in the bottom and, at time t minutes, the depth of water in the tank is x metres. At any instant, the rate at which the depth of the water is decreasing is proportional to the square root of the depth of water in the tank.
So the mark scheme is very vague in regard to the answer to this. I have come up with a solution to the following questions which makes perfect sense to me and is a sensible number yet... wrong.
(1) write down a differential equation which models this situation.
I got : dx/dt= kx^1/2 (which is correct)
(2) when t=0, x=2; when t=5, x=1. Find t when x=0.5.
I integrated with respect to t. Aftere all that I got t=4.5, it is meant to be 8.5 however.
Any help on the second part would be appreciated.