FORENSIC SCIENCE The temperature T of the body of a murder victim found in a room where th...

FORENSIC SCIENCE The temperature T of the body of a murder victim found in a room where the air temperature is 20°C is given by

where t is the number of hours after the victim’s death.

a. Graph the body temperature T (t ) for t ≥ 0. What is the horizontal asymptote of this graph and what does it represent?

b. What is the temperature of the victim’s body after 10 hours? How long does it take for the body’s temperature to reach 25°C?

c. Abel Baker is a clerk in the firm of Dewey, Cheatum, and Howe. He comes to work early one morning and finds the corpse of his boss, Will Cheatum, draped across his desk. He calls the police, and at 8 a.m., they determine that the temperature of the corpse is 33°C. Since the last item entered on the victim’s notepad was, “Fire that idiot, Baker,” Abel is considered the prime suspect. Actually, Abel is bright enough to have been reading this text in his spare time. He glances at the thermostat to confirm that the room temperature is 20°C. For what time will he need an alibi in order to establish his innocence?