A medical examiner called to the scene of a murder will usually take the temperature of the body. A corpse cools at a rate proportional to the difference between its temperature and the temperature of the room. If y(t)is the temperature (in degrees Fahrenheit) of the bodythours after the murder, and if the room temperature is 80, thenysatisfies

y'	=	0.32(y80)
y(0)	=	98.6 (body temperature initially 98.6)

(a) Solve this differential equation and initial condition.

y=

(b) Use your answer to part (a) to estimate how long ago the murder took place if the temperature of the body when it was discovered was 90. [Hint:Find the value oftthat makes your solution equal 90.] (Round your answer to two decimal places.)

t= hr