Problem 2 H 51). The Newton's Law of Cooling says that the rate at which a body cools is proportional tothe difference between the temperature of the body and the temperature of the surrounding medium. I.e., if welet T(t) be the temperature of the body at time t and Tm denotes the temperature of the surrounding medium,thenT()T(t)=k(T(t)- Tm)(1)for some constant k.Suppose the room temperature is 70° F and a cake is 300° F when removed from an oven. Three minuteslater the cake is 200° F. How long will it take to cool the cake to 75° F? [Hint: From (1), the function T(t)is not exponentially decaying; however, consider the function H(t) = T(t) - Tm, and is H(t) an exponentiallydecaying function?]

By Newton's Cooling Law = Proportionality constant Temperature of the surrounding Temperature of the…

Problem 2 H 4). The Newton's Law of Cooling says that the rate at which a body cools is proportional to the difference between the temperature of the body and the temperature of the surrounding medium. Le., if we let T(t) be the temperature of the body at time t and Tm denotes the temperature of the surrounding medium, then T(t) = k(T(t)- Tm) (1) for some constant k. Suppose the room temperature is 70° F and a cake is 300° F when removed from an oven. Three minutes later the cake is 200° F. How long will it take to cool the cake to 75° F? [Hint: From (1), the function T(t) is not exponentially decaying; however, consider the function H(t) = T(t)- Tm, and is H(t) an exponentially decaying function?]

Problem 2 H 4). The Newton's Law of Cooling says that the rate at which a body cools is proportional to the difference between the temperature of the body and the temperature of the surrounding medium. Le., if we let T(t) be the temperature of the body at time t and Tm denotes the temperature of the surrounding medium, then T(t) = k(T(t)- Tm) (1) for some constant k. Suppose the room temperature is 70° F and a cake is 300° F when removed from an oven. Three minutes later the cake is 200° F. How long will it take to cool the cake to 75° F? [Hint: From (1), the function T(t) is not exponentially decaying; however, consider the function H(t) = T(t)- Tm, and is H(t) an exponentially decaying function?]

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Problem 2 H 51). The Newton's Law of Cooling says that the rate at which a body cools is proportional to
the difference between the temperature of the body and the temperature of the surrounding medium. I.e., if we
let T(t) be the temperature of the body at time t and Tm denotes the temperature of the surrounding medium,
then
T()
T(t)=k(T(t)- Tm)
(1)
for some constant k.
Suppose the room temperature is 70° F and a cake is 300° F when removed from an oven. Three minutes
later the cake is 200° F. How long will it take to cool the cake to 75° F? [Hint: From (1), the function T(t)
is not exponentially decaying; however, consider the function H(t) = T(t) - Tm, and is H(t) an exponentially
decaying function?]

Expert Solution

Step 1: Define the problem

By Newton's Cooling Law $fraction numerator d T over denominator d t end fraction equals k open parentheses T minus T subscript m close parentheses$

$rightwards double arrow k$ = Proportionality constant

$rightwards double arrow T subscript m equals$ Temperature of the surrounding

$rightwards double arrow T equals$ Temperature of the cake

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