The dead body of a cricket coach was discovered in a prominent hotel at noon on Sunday where the temperature is 70°F. The temperature of the body at the time of discovery s 76°F and one hour later the temperature is 75.3°F. Newton's law of cooling says that the rate of change of temperature T(t) on an object is proportional the difference between the time T(t) and the temperature Tm of the surrounding medium; that is dT = k(T - Tm) dt Where k is a constant of proportionality. ii 111. Assuming that the coach has a normal body temperature of 98.60F at the time of death, show that T 70+28. 6ekt Show that k≈0.1241 and hence determine the coach's time of death.

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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The dead body of a cricket coach was discovered in a prominent hotel at noon on
Sunday where the temperature is 70°F. The temperature of the body at the time of
discovery s 76°F and one hour later the temperature is 75.3°F. Newton's law of
cooling says that the rate of change of temperature T(t) on an object is proportional
the difference between the time T(t) and the temperature Tm of the surrounding
medium; that is
dT
= k(T - Tm)
dt
Where k is a constant of proportionality.
Transcribed Image Text:The dead body of a cricket coach was discovered in a prominent hotel at noon on Sunday where the temperature is 70°F. The temperature of the body at the time of discovery s 76°F and one hour later the temperature is 75.3°F. Newton's law of cooling says that the rate of change of temperature T(t) on an object is proportional the difference between the time T(t) and the temperature Tm of the surrounding medium; that is dT = k(T - Tm) dt Where k is a constant of proportionality.
ii
111.
Assuming that the coach has a normal body temperature of 98.60F at the time of
death, show that
T
70+28. 6ekt
Show that k≈0.1241 and hence determine the coach's time of death.
Transcribed Image Text:ii 111. Assuming that the coach has a normal body temperature of 98.60F at the time of death, show that T 70+28. 6ekt Show that k≈0.1241 and hence determine the coach's time of death.
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