Ononot — A cup of coffee cools according to \frac{dT}{dt} = -k(T - Ta

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Differential Equationsmedium

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A cup of coffee cools according to $\frac{dT}{dt} = -k(T - T_a)$ . If the ambient temperature $T_a = 20^{\circ}C$ , $T(0) = 90^{\circ}C$ , and $T(1) = 60^{\circ}C$ , find the value of the cooling constant $k$ .