A cake is removed from an oven and its temperature is 350°F. Assume room temperature is 70°F. Five minutes later, the temperature of the cake is 250°F. How long will it take for the cake to cool to 90°F? The rate of change of the temperature of the cake is proportional to the difference between the temperature of the cake and the temperature of the room, so dT(1) 2 =k (T(t)-T„) where T(t) represents the temperature of an object at time t. dt T_ is the temperature of the room. dT(t) 2= k (T(1)-T„) for T(t). dt a) First, solve the differential equation The result should be T(t)=T,,+Ce" .

A cake is removed from an oven and its temperature is 350°F. Assume room temperature is 70°F. Five minutes later, the temperature of the cake is 250°F. How long will it take for the cake to cool to 90°F? The rate of change of the temperature of the cake is proportional to the difference between the temperature of the cake and the temperature of the room, so dT(1) 2 =k (T(t)-T„) where T(t) represents the temperature of an object at time t. dt T_ is the temperature of the room. dT(t) 2= k (T(1)-T„) for T(t). dt a) First, solve the differential equation The result should be T(t)=T,,+Ce" .

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

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