6. a. An elderly patient is running a fever of 39°C one night when her caregiver leaves. At 7 AM the next morning, the p
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6. a. An elderly patient is running a fever of 39°C one night when her caregiver leaves. At 7 AM the next morning, the patient is found to have died from the fever. Her body temperature is taken immediately (at 7 AM) and found to be 35°C. Two hours later (at 9 AM), her body temperature is found to be 33.5°C. The room that she was staying was maintained at a constant temperature of 25°C. Assume that her body is cooled according Newton's Law of cooling, dH = -ka(H - Te), dt where H(t) is the temperature of the body, Te is the room temperature, and ke is the Newton's law cooling constant. Let t = 0 correspond to 7 AM, so H(0) = 35. Solve this differential equation, and use the information at 9 AM (t = 2) to find the value of ka. Estimate the time of death assuming that the patient's temperature was 39°C at the time of death (using normal time, hours and minutes) b. Since heat is lost through the surface, assume that we use a different model for the cooling of the body based on loss of heat through the surface. This model satisfies the differential equation: dH dt -kb(H – Te)2/3 = Once again, solve this differential equation, and use the information at 9 AM (t = 2) to find the value of kb. Estimate the time of death under the same assumption above with this model.