Time of death problem involving a constant variable, K

kinz.kb

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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?
 
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

So, your equation becomes:

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

Is that okay? =]
 
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