8 In a certain chemical reaction, a compound \(A\) is formed from a compound \(B\). The masses of \(A\) and \(B\) at time \(t\) after the start of the reaction are \(x\) and \(y\) respectively and the sum of the masses is equal to 50 throughout the reaction. At any time the rate of increase of the mass of \(A\) is proportional to the mass of \(B\) at that time.
- Explain why \(\frac { \mathrm { d } x } { \mathrm {~d} t } = k ( 50 - x )\), where \(k\) is a constant.
It is given that \(x = 0\) when \(t = 0\), and \(x = 25\) when \(t = 10\). - Solve the differential equation in part (i) and express \(x\) in terms of \(t\).