# Thread: Time of death problem involving a constant variable, K

1. ## Time of death problem involving a constant variable, K

Coroners estimate time of death using the rule of thumb that a body cools about 2 degrees F during the first hour after death and about 1 degree F for each additional hour. Assuming an air temperature of 72 degrees F and a living body temperature of 98.6 degrees F, the temperature T(t) in degrees F of a body at a time t hours since death is given by
T(t) = 72 + 26.6 e^{-kt}.

For what value of k will the body cool by 2 degrees F in the first hour?

I think that the k is throwing me off a bit because I tried plugging in the values and isolating the k but none of my answers are correct. Can someone help please?

2. Originally Posted by kinz.kb
Coroners estimate time of death using the rule of thumb that a body cools about 2 degrees F during the first hour after death and about 1 degree F for each additional hour. Assuming an air temperature of 72 degrees F and a living body temperature of 98.6 degrees F, the temperature T(t) in degrees F of a body at a time t hours since death is given by
T(t) = 72 + 26.6 e^{-kt}.

For what value of k will the body cool by 2 degrees F in the first hour?

I think that the k is throwing me off a bit because I tried plugging in the values and isolating the k but none of my answers are correct. Can someone help please?
T(t) is T(1) and is hence 98.6 - 2 (This is the temperature of the body after 1 hour)

t = 1

$96.6 = 72 + 26.6 e^{-k(1)}$

Is that okay? =]

3. Originally Posted by kinz.kb

I tried plugging in the values and isolating the k but none of my answers are correct.

Maybe you made an arithmetic mistake somewhere?

If you were to show us what you tried, we could show you what went wrong.
.