14 In a chemical reaction, the mass \(m\) grams of a chemical at time \(t\) minutes is modelled by the differential equation
\(\frac { \mathrm { d } m } { \mathrm {~d} t } = \frac { m } { t ( 1 + 2 t ) }\).
At time 1 minute, the mass of the chemical is 1 gram.
- Solve the differential equation to show that \(m = \frac { 3 t } { ( 1 + 2 t ) }\).
- Hence
- find the time when the mass is 1.25 grams,
- show what happens to the mass of the chemical as \(t\) becomes large.