2021 IBSL P1 Q3

Natasha carries out an experiment on the growth of mould. She believes that the growth can be modelled by an exponential function

\(P(t) = A\mathrm{e}^{kt}\)

where \(P\) is the area covered by mould in mm\(^2\), \(t\) is the time in days since the start of the experiment and \(A\) and \(k\) are constants.
The area covered by mould is \(112\) mm\(^2\) at the start of the experiment and \(360\) mm\(^2\) after \(5\) days.

1. Write down the value of \(A\).

   [1]

2. Find the value of \(k\).

   [3]