2025 NASS PRELIMS P1 Q9

The number of cells in an experiment can be modelled by a function \(N(t)=50000\left(1.6^{\frac{t}{2}}\right)\),

where \(t\) is the number of hours that have passed from the start of the experiment.

1. Find the number of cells present at the start of the experiment.[1]
2. Find the time taken for the number of cells to be ten times the initial number of cells. Give your answer to the nearest hour.[3]
3. It is given that the number of cells at time \(t=t_2\) is double the number of cells at the time \(t=t_1\). Show that the difference between the two timings \((t_2-t_1)\) is approximately 2.95 hours, corrected to 3 significant figures.[3]