In Exercise 28 in Section 9.2 we discussed a differential equation that models the temperature of a $95 ^ { \circ } \mathrm { C }$ of coffee in a $20 ^ { \circ } \mathrm { C }$ room. Solve the differential equation to find an expression for the temperature of the coffee at time $t .$
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Step 1:** The differential equation given is: \[\frac{dT}{dt} = -K(T - 20)\] ** Show more…
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In Exercise 28 in Section 9.2 we discussed a differential equation that models the temperature of a $95^{\circ} \mathrm{C}$ cup of coffee in a $20^{\circ} \mathrm{C}$ room. Solve the differential equation to find an expression for the temperature of the coffee at time $t .$
Differential Equations
Separable Equations
In Exercise 9.2.28 we discussed a differential equation that models the temperature of a $ 95^oC $ cup of coffee in a $ 20^oC $ room. Solve the differential equation to find an expression for the temperature of the coffee at time $ t. $
If a cup of coffee has temperature $95^{\circ} \mathrm{C}$ in a room where the temperature is $20^{\circ} \mathrm{C},$ then, according to Newton's Law of Cooling, the temperature of the coffee after $t$ minutes is $T(t)=20+75 e^{-t / 50} .$ What is the average temperature of the coffee during the first half hour?
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