A Thanksgiving turkey with uniform temperature 180 degrees F

A Thanksgiving turkey with uniform temperature 180 degrees Fahrenheit is taken out of an oven and placed in a 70 degrees room. After 5 minutes, the turkey\'s temperature has decreased to 170 degrees. What temperature would we expect the bird to be after another 15 minutes? Use Newton\'s Law of Cooling.

Solution

T(0) = 180 degree Farenheit

t = 5 minutes

Ts = 70 degrees

T(t) = T_s + (T_o - T_s)e^-kt

T(5) = 70 + (180 - 70) e^-k5

^{170 - 70 = 110e^-5k}

^{100/110 = e^-5k}

0.909 = e^-5k

ln 0.909 = -5k

-0.095 = -5k

k = 0.019

T(15) = 70 + (180 - 70)e^-0.019*15

= 70 + 100*0.75

= 70 + 75

= 145 degree

T(15) = 6724.66