9 Compressed air is escaping from a container. The pressure of the air in the container at time \(t\) is \(P\), and the constant atmospheric pressure of the air outside the container is \(A\). The rate of decrease of \(P\) is proportional to the square root of the pressure difference ( \(P - A\) ). Thus the differential equation connecting \(P\) and \(t\) is $$\frac { \mathrm { d } P } { \mathrm {~d} t } = - k \sqrt { } ( P - A )$$ where \(k\) is a positive constant.

1. Find, in any form, the general solution of this differential equation.
2. Given that \(P = 5 A\) when \(t = 0\), and that \(P = 2 A\) when \(t = 2\), show that \(k = \sqrt { } A\).
3. Find the value of \(t\) when \(P = A\).
4. Obtain an expression for \(P\) in terms of \(A\) and \(t\).