A cup of tea is poured at an initial temperature of and left to cool in a dining hall

MATHEMATICS · Multi-part · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

A cup of tea is poured at an initial temperature of

95^{\circ}\text{C}

and left to cool in a

20^{\circ}\text{C}

dining hall. Five minutes later, the tea’s temperature has fallen to

70^{\circ}\text{C}

. Let

T(t)

denote the temperature (in

^{\circ}\text{C}

) of the tea

t

minutes after it is poured. (a) Determine the value of the proportionality constant

k

(in \text{min}^{-1}) that governs the cooling process for this cup of tea. (b) Using your value of

k

, predict the tea’s temperature 15 minutes after it is poured. Give your answer to the nearest tenth of a degree Celsius. (c) Interpret the sign of

k

in the context of this cooling scenario.