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?