Chapter 4.3, Problem 12E

Reminder Round all answers to two decimal places unless otherwise indicated.

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 round 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 $D=D\left(t\right)$ 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 P.M.)

$t=hours$ since 3:00 P.M.	$D=temperaturedifference$
$0$	$26.83$
$1$	$24.42$
$2$	$22.22$
$3$	$20.22$
$4$	$18.40$
$5$	$16.74$

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?