Mathematics

Problem

A cup of coffee is initially

85^{\circ}\text{C}

and cools in a room kept at

22^{\circ}\text{C}

. Eight minutes later, the coffee’s temperature is

70^{\circ}\text{C}

. Determine the value of the proportionality constant

k

(in

\text{min}^{-1}

) in the temperature model for this situation.