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 body t hours after the murder, and if the room temperature is 60, then y satisfies y' = -0.32(y-60) 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 80. [Hint: Find the value of t that makes your solution equal 80.] (Round your answer to two decimal places.) t = hr