9 The variables \(x\) and \(t\) satisfy the differential equation \(5 \frac { \mathrm {~d} x } { \mathrm {~d} t } = ( 20 - x ) ( 40 - x )\). It is given that \(x = 10\) when \(t = 0\).
- Using partial fractions, solve the differential equation, obtaining an expression for \(x\) in terms of \(t\). [9]
- State what happens to the value of \(x\) when \(t\) becomes large.