4 The temperature \(\theta ^ { \circ } \mathrm { C }\) of water in a container after \(t\) minutes is modelled by the equation $$\theta = a - b \mathrm { e } ^ { - k t } ,$$ where \(a , b\) and \(k\) are positive constants.
The initial and long-term temperatures of the water are \(15 ^ { \circ } \mathrm { C }\) and \(100 ^ { \circ } \mathrm { C }\) respectively. After 1 minute, the temperature is \(30 ^ { \circ } \mathrm { C }\).

1. Find \(a , b\) and \(k\).
2. Find how long it takes for the temperature to reach \(80 ^ { \circ } \mathrm { C }\).