A thermometer is moved from a room where the temperature is 68 °F to a freezer where the temperature is 12 °F. After 30 seconds the thermometer reads 53 °F. Let T(t) denote the temperature, in Fahrenheit, at time t, in seconds. Using Newton's cooling law: T'(t) - k(T(t) – Tm(t) to answer the questions. (a) Write a differential equation for T(t). The only unknown should be T(t). T'(t) : (b) What does the thermometer read after 2 minutes? °F (c) Compute the limit. lim T(t)
A thermometer is moved from a room where the temperature is 68 °F to a freezer where the temperature is 12 °F. After 30 seconds the thermometer reads 53 °F. Let T(t) denote the temperature, in Fahrenheit, at time t, in seconds. Using Newton's cooling law: T'(t) - k(T(t) – Tm(t) to answer the questions. (a) Write a differential equation for T(t). The only unknown should be T(t). T'(t) : (b) What does the thermometer read after 2 minutes? °F (c) Compute the limit. lim T(t)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Question 6**
A thermometer is moved from a room where the temperature is 68°F to a freezer where the temperature is 12°F. After 30 seconds the thermometer reads 53°F. Let \( T(t) \) denote the temperature, in Fahrenheit, at time \( t \), in seconds.
Using Newton's cooling law:
\[ T'(t) = -k(T(t) - T_m(t)) \]
to answer the questions.
**(a)** Write a differential equation for \( T(t) \). The only unknown should be \( T(t) \).
\[ T'(t) = \]
**(b)** What does the thermometer read after 2 minutes?
\[\_\_\_\_\] °F
**(c)** Compute the limit.
\[ \lim_{t \to \infty} T(t) = \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa043fe4-4451-42e8-82d1-21cc59f9ce63%2F591df100-0016-4cd1-b180-6914731d7f94%2F8rd4tgj_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 6**
A thermometer is moved from a room where the temperature is 68°F to a freezer where the temperature is 12°F. After 30 seconds the thermometer reads 53°F. Let \( T(t) \) denote the temperature, in Fahrenheit, at time \( t \), in seconds.
Using Newton's cooling law:
\[ T'(t) = -k(T(t) - T_m(t)) \]
to answer the questions.
**(a)** Write a differential equation for \( T(t) \). The only unknown should be \( T(t) \).
\[ T'(t) = \]
**(b)** What does the thermometer read after 2 minutes?
\[\_\_\_\_\] °F
**(c)** Compute the limit.
\[ \lim_{t \to \infty} T(t) = \]
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