1. ## Exponential function about determing the time of death.

Using Newton's Law of Cooling, I have to predict the time of death of a person.

H-R = Be^-kt is the relationship between the temperature of the body (H) and the constant room temperature (R), t is the time in hours since the body expired and k and B are the constants. Using that equation I have to determine the time of death.

When the murder is committed, the body, originally at 37'C, cools according to Newton's Law of Cooling, if the body is found at 9:30am the temperature of the body is 35'C and that temperature of the body is 30'C at 4:00pm. Assuming that the temperature of the surrounding air is a constant 20'C.

I know how to solve simpler exponential models, but I'm confused how to do this one.

2. Originally Posted by eriiin
Using Newton's Law of Cooling, I have to predict the time of death of a person.

H-R = Be^-kt is the relationship between the temperature of the body (H) and the constant room temperature (R), t is the time in hours since the body expired and k and B are the constants. Using that equation I have to determine the time of death.

When the murder is committed, the body, originally at 37'C, cools according to Newton's Law of Cooling, if the body is found at 9:30am the temperature of the body is 35'C and that temperature of the body is 30'C at 4:00pm. Assuming that the temperature of the surrounding air is a constant 20'C.

I know how to solve simpler exponential models, but I'm confused how to do this one.
At $\displaystyle t_0=0$ we have:

$\displaystyle H-R=17=Be^0=B$

So $\displaystyle B=17$.

At $\displaystyle t=9.5$ (we are working in decimal hours here):

$\displaystyle H-R=15=17e^{-k(9.5-t_0)}$

At $\displaystyle t=16.0$ (4 pm is 16.00hrs):

$\displaystyle H-R=10=17e^{-k(16.0-t_0)}$

Now take logs and solve the resulting equations for $\displaystyle $$t_0 and \displaystyle$$ k$

CB

3. I'm a little confused, what does the o in to mean? And why is it 17d^-k(9.5-t)?

4. Originally Posted by eriiin
I'm a little confused, what does the o in to mean? And why is it 17d^-k(9.5-t)?
$\displaystyle $$t_0 denotes the time of death The second question I don't understand, \displaystyle$$ 9.5$ hours is 09:30 so $\displaystyle 9.5-t_0$ is the time since death at 09:30 in hours

CB

5. Sorry I should have been more specific, I just don't understand why it's 9.5 - t, like why is that we subtract it?

6. Originally Posted by eriiin
Sorry I should have been more specific, I just don't understand why it's 9.5 - t, like why is that we subtract it?
It is the time from death at 09:30

CB

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# help coroners to determine time of death using exponential function

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