6. The mass, \(m\) grams, of a radioactive substance \(t\) years after first being observed, is modelled by the equation
$$m = 25 \mathrm { e } ^ { 1 - k t }$$
where \(k\) is a positive constant.
- State the value of \(m\) when the radioactive substance was first observed.
Given that the mass is 50 grams, 10 years after first being observed,
- show that \(k = \frac { 1 } { 10 } \ln \left( \frac { 1 } { 2 } \mathrm { e } \right)\)
- Find the value of \(t\) when \(m = 20\), giving your answer to the nearest year.