Its Amanda\'s birthday and Shane is baking her a cake. He takes the cake out of

Question

Its Amanda's birthday and Shane is baking her a cake. He takes the cake out of the 350 F oven into the room with a temperature of 65 F. The cooling of the cake is modeled by the following equation

T(t)=Tr+(To?Tr)e^kt

where T(t) is the temperature of the cake t minutes after it has been taken out of the oven, Tr is the temperature of the cake's present surroundings and To is the cakes initial temperature.

a) Write a model for the temperature of the cake. Find the constant k.

b) What is the temerature of the cake after 1 hour ?

Explanation / Answer

T(t)=65+(350-65)e^kt by differentiating both sides and equating dT(t)/dt at t= 0 to 350-65 we get k = 1

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