Cooling modelled by exponential decay towards room temperature: initial value, rate constant and time to reach a temperature

A cup of tea is left on a table to cool. Its temperature \(t\) minutes later is \(\Theta\,^\circ\mathrm{C}\), where

\(\Theta=22+68\mathrm{e}^{-kt},\quad t\geq0,\)

Here \(k>0\) is a constant.

1. Write down the temperature of the tea when it is first left to cool.[1]

Ten minutes after it is left, the temperature of the tea is \(55\,^\circ\mathrm{C}\).

2. Find \(k\).[2]
3. Find how long it takes for the temperature of the tea to fall to \(30\,^\circ\mathrm{C}\).[2]