2026 NASS P1 Q8

The chickens in a farm are infected by a certain bird flu. The number of chickens (in thousands) in the farm is modelled by \(N=\dfrac{27}{2+\alpha t\mathrm e^{\beta t}}\), where \(t\) is the number of days elapsed since the start of the spread of the bird flu and \(\alpha\) and \(\beta\) are constants.

1. Express \(\ln\left(\dfrac{27-2N}{Nt}\right)\) as a linear function of \(t\) in terms of \(\alpha\) and \(\beta\).[4]
2. It is given that the slope and the intercept on the horizontal axis of the graph of the linear function obtained in (a) are \(-0.1\) and \(10\ln0.03\) respectively.
   Find \(\alpha\) and \(\beta\).[3]