Newton's Law of Cooling (Calculating Time of Death)

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Homework Help Overview

The problem involves applying Newton's Law of Cooling to determine the time of death based on the temperature of a corpse found in a freezer. The context includes specific temperatures and the need to solve for time using a given formula.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss rearranging the formula and taking logarithms to solve for time. There is a question about the correctness of the calculated time and a request for confirmation of the solution.

Discussion Status

Some participants have provided guidance on manipulating the equation and evaluating logarithms. There is a mix of attempts to verify the solution, with one participant expressing uncertainty about their result.

Contextual Notes

Participants are working with specific temperature values and a formula that may require careful handling of logarithmic properties. The discussion reflects a focus on confirming calculations rather than resolving the problem definitively.

JacksonSolo
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Homework Statement



The problem states that you discovered the body at 1pm Thursday in a freezer where the temperature was 10F. Temperature of the corpse at discovery was 40F. I have to find how many hours ago the victim died.

Homework Equations



You are given the formula T = Ta + (98.6 - Ta)(0.97)^t where Ta is air temperature.

The Attempt at a Solution



So I plugged the numbers in: 40 = 10 + (98.6-10)(0.97)^t but I have no idea how to solve for t. Any help?
 
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Move the constants to one side and take logs on both sides you should get:

t log(0.97) = log \frac{30}{88.6}

Evaluate that for t.
 
Ok so I get the log of 30/88.6 and divide that by the log of 0.97 to get t, which equals 35.55 hours. Did I do that right?
 
Im just looking for confirmation i solved the problem right.
 
It appears correct to me. But the answer is actually... 1:45 am on Wednesday?
 
Last edited:
Ok thanks. Yes, true ;)
 

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