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We recall Newton’s law of cooling. If E is the ambient temperature and T = T(t) is the temperature of an object at time t, then the rate of change of T is proportional to the temperature difference. That is, T(t) satisfies the differential equation dT dt = k(E − T). (1) Verify that the function T(t) = E + (T0 − E)e −kt (2) satisfies equation (1), where E and T0 are constants. (It is a fact that, up to the values of E and T0, this is the only solution to (1).

We recall Newton’s law of cooling. If E is the ambient temperature and T = T(t) is the temperature of an object at time t, then the rate of change of T is proportional to the temperature difference. That is, T(t) satisfies the differential equation dT dt = k(E − T). (1) Verify that the function T(t) = E + (T0 − E)e −kt (2) satisfies equation (1), where E and T0 are constants. (It is a fact that, up to the values of E and T0, this is the only solution to (1).

Calculus: Early Transcendentals
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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We recall Newton’s law of cooling. If E is the ambient temperature and T = T(t) is the temperature of an object at time t, then the rate of change of T is proportional to the temperature
difference. That is, T(t) satisfies the differential equation
dT
dt = k(E − T). (1)
Verify that the function
T(t) = E + (T0 − E)e
−kt (2)
satisfies equation (1), where E and T0 are constants. (It is a fact that, up to the values of E and
T0, this is the only solution to (1).

Find the temperature T(t) of the body at t hours after the murder, for t > 0. Estimate the number of minutes body had lain dead before it was discovered.
Transcribed Image Text:Find the temperature T(t) of the body at t hours after the murder, for t > 0. Estimate the number of minutes body had lain dead before it was discovered.
We recall Newton's law of cooling. If E is the ambient temperature and T = T(t) is the tem- perature of an object at time t, then the rate of change of T is proportional to the temperature difference. That is, T(t) satisfies the differential equation dT = k(E – T). dt (1) Verify that the function -kt T(t) = E+ (To - (2) satisfies equation (1), where E and To are constants. (It is a fact that, up to the values of E and To, this is the only solution to (1).) 2. One summer afternoon, when the ambient temperature was 20° C, the body of a murder victim was found. At the time of the murder (when t = 0), the victim had normal body temperature (37° C). When the body was found (at time t = a, in hours) the body's temperature was mea- sured to be T(a) farther, to 25° C. = 30° C. One hour after the body was discovered, its temperature had dropped Continued on next page ...
Transcribed Image Text:We recall Newton's law of cooling. If E is the ambient temperature and T = T(t) is the tem- perature of an object at time t, then the rate of change of T is proportional to the temperature difference. That is, T(t) satisfies the differential equation dT = k(E – T). dt (1) Verify that the function -kt T(t) = E+ (To - (2) satisfies equation (1), where E and To are constants. (It is a fact that, up to the values of E and To, this is the only solution to (1).) 2. One summer afternoon, when the ambient temperature was 20° C, the body of a murder victim was found. At the time of the murder (when t = 0), the victim had normal body temperature (37° C). When the body was found (at time t = a, in hours) the body's temperature was mea- sured to be T(a) farther, to 25° C. = 30° C. One hour after the body was discovered, its temperature had dropped Continued on next page ...
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