(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A forensic specialist took the temperature of a victim's body lying in a street at 2:10 AM and found it to be 85.7° F. At 2:40 AM, the temperature of the body was 84.8° F. When was the murder committed if the air temperature during the night was 55° F? Remember, normal body temperature is 98.6° F.

2. Relevant equations

I think I'm supposed to use Newton's Law of Cooling:

T = T_{s}+ (T_{o}- T_{s})e^{-kt}

Where

T is any temperature

T_{s}is the surrounding temperature

T_{o}is the original temperature

3. The attempt at a solution

I know I should solve for k first, and then substitute it into the original equation to get t, but I'm not sure what to do once I get t.

84.8 = 55 + (85.7 - 84.8)e^{-k30}because the difference between 2:10 and 2:40 is 30 minutes.

(84.8 - 55)/(85.7 - 84.8) = e^{-k30}

ln(2.37984) = lne^{-k30}

ln(2.37984)/30 = -k

k = -.116662

Then

85.7 = 55 + (98.6 - 85.7)e^{.116662*t}

(85.7 - 55)/(98.6 - 85.7) = e^{.116662*t}

ln(2.37984) = lne^{.116662*t}

ln(2.37984)/.116662 = t

t = 7.43203

But how do I put that into a time format?

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# Homework Help: Temperature question

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