8 A cylindrical tank is initially full of water. There is a small hole at the base of the tank out of which the water leaks. The height of water in the tank is \(x \mathrm {~m}\) at time \(t\) seconds. The rate of change of the height of water may be modelled by the assumption that it is proportional to the square root of the height of water. When \(t = 100 , x = 0.64\) and, at this instant, the height is decreasing at a rate of \(0.0032 \mathrm {~ms} ^ { - 1 }\).

1. Show that \(\frac { \mathrm { d } x } { \mathrm {~d} t } = - 0.004 \sqrt { x }\).
2. Find an expression for \(x\) in terms of \(t\).
3. Hence determine at what time, according to this model, the tank will be empty.