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Differential Equationsmedium
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A cup of coffee cools according to dTdt=−k(T−Ta)\frac{dT}{dt} = -k(T - T_a)dtdT​=−k(T−Ta​). If the ambient temperature Ta=20∘CT_a = 20^{\circ}CTa​=20∘C, T(0)=90∘CT(0) = 90^{\circ}CT(0)=90∘C, and T(1)=60∘CT(1) = 60^{\circ}CT(1)=60∘C, find the value of the cooling constant kkk.