2 The temperature \(T\) in degrees Celsius of water in a glass \(t\) minutes after boiling is modelled by the equation \(T = 20 + b \mathrm { e } ^ { - k t }\), where \(b\) and \(k\) are constants. Initially the temperature is \(100 ^ { \circ } \mathrm { C }\), and after 5 minutes the temperature is \(60 ^ { \circ } \mathrm { C }\).

1. Find \(b\) and \(k\).
2. Find at what time the temperature reaches \(50 ^ { \circ } \mathrm { C }\).