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?

Question

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?

dumbcow · Answer

plug in all the given information to solve for k
T(t) = 325
T_0 = 350
T_r = 65
t = 3
$$325 = 65 +(350-65)e^{3k}$$

anonymous · Answer

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

anonymous · Answer

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