2025 MSHS PRELIMS P2 Q3

The decay of a certain radioactive isotope can be modelled by the exponential equation \(N=N_0e^{-at}\) after \(t\) weeks, where \(N\) represents the amount of radioactive isotope, \(N_0\) and \(a\) are constants. A sample of this radioactive isotope has a mass of 100.9 g initially. After 2 weeks, it is found that the amount of this sample left is 84.6 g.

1. Calculate the value of \(a\).[3]
2. What percentage of this sample has decayed after 5 weeks?[3]
3. Find the number of weeks when the amount of radioactive isotope decayed first exceeds 60 g. Give your answer correct to the nearest week.[3]