A cook has finished baking a cake and placed it on the bench to cool. The temperature in the room is 20°C and the temperature of the cake when it was taken out of the oven is 160°C (a) Given that the temperature of the cake is governed by Newton's law of cooling, write down a differential equation governing T(t), the temperature of the cake after t hours. What is the appropriate initial condition? (Newton's law of cooling: dT dt =-K(T-Ta), where K is a constant and Ta is the ambient temperature.) (b) From you answer in part (a), derive the solution T(t) = 20 + 140e Kt, where K is a (c) constant. Given that the cake has cooled to 90°C after 1 hour, determine the constant K. (d) The cook decides that the cake is cool enough to be taken out of the cake pan when its temperature lowers to 40 degrees C. Find when this will happen, both in exact form and as a decimal approximation to at least 2 decimal places, showing all working.

A cook has finished baking a cake and placed it on the bench to cool. The temperature in the room is 20°C and the temperature of the cake when it was taken out of the oven is 160°C (a) Given that the temperature of the cake is governed by Newton's law of cooling, write down a differential equation governing T(t), the temperature of the cake after t hours. What is the appropriate initial condition? (Newton's law of cooling: dT dt =-K(T-Ta), where K is a constant and Ta is the ambient temperature.) (b) From you answer in part (a), derive the solution T(t) = 20 + 140e Kt, where K is a (c) constant. Given that the cake has cooled to 90°C after 1 hour, determine the constant K. (d) The cook decides that the cake is cool enough to be taken out of the cake pan when its temperature lowers to 40 degrees C. Find when this will happen, both in exact form and as a decimal approximation to at least 2 decimal places, showing all working.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.7: Exponential And Logarithmic Models

Problem 4SE: Define Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of...

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