IP3 Class Test (May 2025) Q9 (2023 ACSBR AM Prelim P1 Q3)

The temperature, \(T^\circ\mathrm{C}\), of glass being heated in a kiln is given by the formula \(T = 2030 - 2000e^{-kt}\), where \(t\) is the time in hours since the glass was placed in the kiln. The temperature of the glass after \(90\) minutes is \(1000^\circ\mathrm{C}\).

1. Find the temperature of the glass before it was heated.[1]
2. The glass can be moulded into different shapes when its temperature reaches at least \(1300^\circ\mathrm{C}\). What is the earliest time that the glass can be removed from the kiln and moulded?[4]
3. The instruction manual of the kiln gives the range of the temperature of the kiln as \(T < y^\circ\mathrm{C}\). State the value of \(y\).[1]