A bald eagle murder mystery: At 3:00 P.M. a park ranger discovered a dead bald eagle that had been impaled by an arrow. Only two archers were found in the region. The first archer is able to establish...

A bald eagle murder mystery: At 3:00 P.M. a park ranger discovered a dead bald eagle that had been impaled by an arrow. Only two archers were found in the region. The first archer is able to establish that between 11:00 A.M. and 1:00 P.M., he was in a nearby diner having lunch. The second archer can show that he was in camp with friends between 9:00 A.M. and 11:00 A.M. The air temperature in the park has remained at a constant 62 degrees. Beginning at 3:00 P.M., the difference D = D(t) between the temperature of the dead eagle and that of the air was measured and recorded in the following table. (Here t is the time in hours since 3:00 P.M.)\

This table, together with the fact that the body temperature of a living bald eagle is 105 degrees, exonerates one of the archers, but the other may remain a suspect. Which archer’s innocence is established?