# Temperature question

1. Feb 22, 2012

### theintarnets

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 = Ts + (To - Ts)e-kt

Where
T is any temperature
Ts is the surrounding temperature
To 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?

2. Feb 22, 2012

### eumyang

You have a mistake in bold. The temperature of the surrounding medium should go there, so it's 55, not 84.8.

Same thing here.

Even though the number in bold is wrong, I'm not sure how you got 2.37984.

Last edited: Feb 22, 2012