It’s Amanda’s birthday and Shane is baking her a cake. He takes the cake out of the 350◦ F oven into the room with temperature of 65◦ F . The cooling of the cake is modeled by the following equation:
T (t) = T_r + (T_0 − T_r )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 T0 is the cake’s initial temperature. In 3 minutes, the cake cools oﬀ down to 325◦ F .
(a) Write a model for the temperature of the cake. Find the constant k.
(b) What is the temperature of the cake after 1 hour?

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a negative answer for k (-.031), would be correct?

and for part b) would if look like this: T(t) = 65 + (350-65)e^(60k) ?

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