Math 171 word problems

Question

A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a table in a room where the temperature is 75 Fahrenheit. Give answers accurate to at least 2 decimal places.

(a) If the temperature of the turkey is 154 Fahrenheit after half an hour, what is its temperature after 45 minutes?

Answer 1

Let T(t) = temperature after t minutes

 

By Newton's Law of Cooling, T(t) = 75 + (185-75)e^kt = 75 + 110e^kt

 

(a). T(30) = 75 + 110e^30k = 154

 

             110e^30k = 79

 

               e^30k = 0.7181818

 

                30k = ln(0.7181818)

 

                  k = -0.0110344551

 

   T(t) = 75 + 110e^{-0.0110344551t}

 

   So, T(45) = 75 + 110e^{-0.0110344551(45)} ≈ 142°