question archive We recall Newton's law of cooling
We recall Newton's law of cooling
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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
(1). dT/dt = k(E − T)
(a) [3 points] Verify that the function (2).T(t) = E + (T0 − E)e −kt
satisfies equation (1), assuming that the ambient temperature E is constant. (It is a fact that, up to the value of T0, this is the only solution to (1) when E is constant.)
(b) One summer afternoon, when the ambient temperature was 20? C, the body of a murder victim was discovered. 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 measured to be T(a) = 30? C. One hour after the body was discovered, its temperature had dropped farther, to 25? C. ] Find the temperature T(t) of the body at t hours after the murder, for t ≥ 0.
c)] Estimate the number of minutes body had lain dead before it was discovered
