Exponential cooling model: initial temperature, rate constant from one reading and the time to reach a given temperature

Hot tea is poured into a cup. The temperature of the tea, \(\theta\ ^\circ\text{C}\), \(t\) minutes after it is poured is modelled by \(\theta(t)=22+68e^{-kt}\), for \(t\geq0\), where \(k>0\) is a constant.

1. Write down the temperature of the tea at the moment it is poured.[1]
2. Five minutes after it is poured, the temperature of the tea is \(65^\circ\text{C}\).
   Find \(k\).[2]
3. Find the time taken for the temperature of the tea to fall to \(40^\circ\text{C}\).[2]