Thread: 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.

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 we have:



So .

At (we are working in decimal hours here):



At (4 pm is 16.00hrs):



Now take logs and solve the resulting equations for and

CB

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

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)?

denotes the time of death

The second question I don't understand, hours is 09:30 so is the time since death at 09:30 in hours

CB

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?

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