Answer: Estimate Murder Time from Temp & Air: 55°F

[theintarnets]

Homework Statement

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.

Homework 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

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?

 

[eumyang]

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

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

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

Same thing here.

(84.8 - 55)/(85.7 - 84.8) = e^-k30
ln(2.37984) = lne^-k30

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