2025 SCGS PRELIMS P2 Q1

In an experiment, 5 million cells were stored in a container. It was observed that 40% of the cells are dying every minute. The number of cells remaining, \(N\), after \(t\) minutes, is given by \(N = Ae^{kt}\), where \(A\) and \(k\) are constants.

1. Explain why \(k = \ln \frac{3}{5}\).[2]
2. Find the time taken when the number of cells decreases to 2000.[3]