You come into your professor's office to ask some questions shortly before 9:00 a.m. on Friday.

You find him lying on the floor of his office in a pool of chalk dust, dead.

You quickly call the police and their investigators take several measurements over the next hour, including:
1) the body temperature at 9:00 a.m. - 80 degrees.
2) the body temperature at 10:00 a.m. - 78 degrees
3) room temperature - 70 degrees (constant)

You realize that the police believe you to be a prime suspect, so you need an alibi. You know that you were studying with friends until 3:00 a. m., but you aren't sure if that is enough information. You need to know the time of death!

Assuming that the difference between body temperature and room temperature changes at a rate proportional to that difference, and that the normal body temperature is 98.6 degrees, how good is your alibi?

(In reply to solution (spoiler) by Daniel)

just thought I'd show how I got T(x)=k*a^x.  from the explanation dT/dx=-k*T  and solving this differential equation and rearranging k and the constant from integration you see that T(x)=k*a^x

Posted by Daniel on 2008-08-31 13:52:25