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10-141.
1. According to Newton’s law of cooling, the rate at which an object cools (or warms) is directly proportional to the temperature difference between the environment and the object itself. Three years ago the corpse of Dr. Deadman was discovered in the coroner’s office. The room temperature of the coroner’s office was (17ºC). The doctor’s body temperature was measured to be 27°C, which was 10°C below normal. Homework Help ✎

1. Dr. Deadman’s body was found at 5:05 p.m. An hour later the body had cooled to 26ºC. At what rate was the body cooling when it was found?

2. Approximately when was Dr. Deadman killed?

$\frac{dT}{dt}=-k(T-17)$

After solving the differential equation:

$T(t)=Ce^{-kt}+17$

Now use (0, 27) and (1, 26) to solve for the values of the parameters.

What is T′(0)?

Normal body temperature is 37ºC.