5 In a certain industrial process, a substance is being produced in a container. The mass of the substance in the container \(t\) minutes after the start of the process is \(x\) grams. At any time, the rate of formation of the substance is proportional to its mass. Also, throughout the process, the substance is removed from the container at a constant rate of 25 grams per minute. When \(t = 0 , x = 1000\) and \(\frac { \mathrm { d } x } { \mathrm {~d} t } = 75\).

1. Show that \(x\) and \(t\) satisfy the differential equation $$\frac { \mathrm { d } x } { \mathrm {~d} t } = 0.1 ( x - 250 )$$
2. Solve this differential equation, obtaining an expression for \(x\) in terms of \(t\).