A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F. (Round your answers to the nearest whole number.)

Question

a) If the temperature of the turkey is 150°F after half an hour, what is the temperature after 45 minutes?

b) When will the turkey have cooled to 95°F?

Answer 1

This is the Newton's law of cooling.

T(t) = the temperature of turkey after t minutes

The difference of T and the surrounding temperature of 75F will follow an exponential decay model:

T(t) - 75 = (T₀ - 75) e^kt, where T₀ = 185F is the initial turkey temperature at time t = 0 minutes.

T(t) - 75 = 110 e^kt.

Find k:

At 30 minutes: T(30) - 75 = 150 - 75 = 75 = 110 e^30k

k = (1/30)ln(75/110) = -0.012766

So your model is: T(t) = 75 + 110e^-0.012766t

(a) Evaluate T(45).

(b) Solve the equation T(t) = 75 + 110e^-0.012766t = 95

The answer t will be in minutes.