10 A certain substance is formed in a chemical reaction. The mass of substance formed \(t\) seconds after the start of the reaction is \(x\) grams. At any time the rate of formation of the substance is proportional to \(( 20 - x )\). When \(t = 0 , x = 0\) and \(\frac { \mathrm { d } x } { \mathrm {~d} t } = 1\).
- Show that \(x\) and \(t\) satisfy the differential equation
$$\frac { \mathrm { d } x } { \mathrm {~d} t } = 0.05 ( 20 - x ) .$$
- Find, in any form, the solution of this differential equation.
- Find \(x\) when \(t = 10\), giving your answer correct to 1 decimal place.
- State what happens to the value of \(x\) as \(t\) becomes very large.
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