The temperature of water in a tea cup, \(T\,^\circ\mathrm{C}\), \(t\) minutes after boiling water is poured into the empty cup can be modelled by the formula \(T = 25 + 75\mathrm{e}^{-kt}\).
The diagram above shows the ideal brewing temperatures for various teas at a particular teahouse. At this teahouse, green tea leaves are placed into the tea cup for brewing at the ideal temperature when \(t = 6\).
Determine whether the teahouse's standards for brewing tea would be adhered to if black tea leaves are placed into the teacup when \(t = 2\).[4]
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