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**URGENT! Newton's law of cooling to find time of death**

## Homework Statement

The victim, Peter Sloane (a senior physics lecturer), was discovered at 9.43pm with a liver temperature of 22.26°C in the Oliver Lodge coffee room, with the window open. The temperature of the room matched that of the outside. After checking weather reports, it was found that at precisely 9.43pm, the temperature outside was 17°C, however, it had steadily been dropping by approximately 1°C every hour before this. The temperature for the rest of the day had been constant at 20°C until it started to drop. Cause of death was determined to be heavy metal poisoning. (No puns please, that's how it's stated...) Using the equation for Newton’s law (given*previously), determine how*long Peter had been dead when he was found, and consequently, his time of death.

## Homework Equations

Newton's law of Cooling:

T(t) = Te+ (T0− Te)e^−kt

Where T(t)= temperature with respect to time

Te= Temperature of surrounding environment

T0= Initial temperature (when t=0)

k= constant, worked out previously as 0.0070636

t= time

## The Attempt at a Solution

I have no idea where to start. The paper gives nothing about the initial body temperature, but even if I take that to be 37 degrees C, I'm pretty sure I can't just take natural logs, because Te isn't constant over the previous 3 hours, and it's due in tomorrow morning... Help!

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