We know from Newton's Law of Cooling that the rate at which an object warms up is proportional to the difference between the ambient temperature of the room and the temperature of the object. The differential equation corresponding to this situation is given by y=k(My) where k is a positive constant. The solution to this equation is given by y=M+(y0M)e^(kt), where y0 is the initial temperature of the object.

Suppose your Thanksgiving turkey is kept at a temperature of 40 degrees Fahrenheit until it is put into a 350 degrees Fahrenheit oven. It takes 2 hours for the turkey to warm up to a safe eating temperature of 165 degrees Fahrenheit. Find the values of y0, M, and k, for this situation,round your answers to 3 decimal place.

y0 = ?

M= ?

k= ?

Regardless of your answers above, suppose the kk value in this situation is k=0.3. Find the initial rate of increase of the turkey's temperature as soon as it is placed in the oven.

_____?___ Round to 3 decimal places. Answer degrees per hour.