2021 MSS AM S4 Q6

In an experiment, \(200\) grams of a particular radioactive substance is stored in a container. The amount of substance present after \(t\) days is given by \(N = 200e^{kt}\), where \(k\) is a constant. It is found that the substance is halved after \(20\) days.

1. Find the amount of substance remaining after \(1\) week.[4]

The radioactive substance is considered to be safe to be discarded using the proper procedures when the amount is reduced to \(15\) grams.

2. John claimed that it is safe to discard the radioactive substance after \(74\) days. Is his claim justified? Show the calculations and the reasons on which you based your answer.[2]