The decay of a certain radioactive isotope can be modelled by the exponential equation \(N=N_0e^{-at

Question

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 $84.6 g$. Calculate the value of a.[3] What percentage of this sample has decayed after 5 weeks?[3] Find the number of weeks when the amount of radioactive isotope decayed first exceeds $60 g$. Give your answer to the nearest week.[3]

Accepted Answer

(a)a=0.0881 (b)35.6% (c)11 weeks

2025 MSHS PRELIMS P2 Q3

2025 MSHS PRELIMS P2 Q3