5. The mass, \(m\) grams, of a radioactive substance, \(t\) years after first being observed, is modelled by the equation
$$m = 25 \mathrm { e } ^ { - 0.05 t }$$
According to the model,
- find the mass of the radioactive substance six months after it was first observed,
- show that \(\frac { \mathrm { d } m } { \mathrm {~d} t } = k m\), where \(k\) is a constant to be found.