A piece of chicken is boiled until its internal temperature reaches 165 °F. The chicken is then transferred to a refrigerator held at 49 °F to cool down. The internal temperature of the chicken at time t is given by T(t), and the temperature obeys Newton's law dT = −k(T - Tm) where Tm is the temperature of the refrigerator and k > 0 is a constant. After 5 minutes in the refrigerator, the internal temperature of the chicken is 155 °F. How long will it take for the temperature of the chicken to reach 70 °F?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A piece of chicken is boiled until its internal temperature reaches 165 °F. The chicken is then transferred to a
refrigerator held at 49 °F to cool down. The internal temperature of the chicken at time t is given by T(t), and the
temperature obeys Newton's law
dT
=
-k(T - Tm)
where Tm is the temperature of the refrigerator and k > 0 is a constant.
After 5 minutes in the refrigerator, the internal temperature of the chicken is 155 °F. How long will it take for the
temperature of the chicken to reach 70 °F?
Transcribed Image Text:A piece of chicken is boiled until its internal temperature reaches 165 °F. The chicken is then transferred to a refrigerator held at 49 °F to cool down. The internal temperature of the chicken at time t is given by T(t), and the temperature obeys Newton's law dT = -k(T - Tm) where Tm is the temperature of the refrigerator and k > 0 is a constant. After 5 minutes in the refrigerator, the internal temperature of the chicken is 155 °F. How long will it take for the temperature of the chicken to reach 70 °F?
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