George Dunn
07/14/2023 · Elementary School
The differential equation below models the temperature of a \( 95^{\circ} \mathrm{C} \) cup of coffee in a \( 21^{\circ} \mathrm{C} \) room, where it is known that the coffee cools at a rate of \( 1^{\circ} \mathrm{C} \) per minute whi temperature of the cup of coffee in \( { }^{\circ} \mathrm{C} \) and let \( t \) be the time in minutes, with \( t=0 \) corresponding to the time when the temperature was \( 95^{\circ} \mathrm{C} \).) \[ \frac{d y}{d t}=-\frac{1}{50}(y-21) \]
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The solution to the differential equation is \( y(t) = 74 e^{-\frac{1}{50} t} + 21 \).
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