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Question

This exercise uses Newton's Law of Cooling.

A roasted 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 76°F.

Find the following values for Newton's Law of Cooling

(T(t) = Ts + D0e−kt),

where time is measured in minutes and the temperature is measured in degrees Fahrenheit, if the temperature of the turkey is 155°F after half an hour.

Ts

=

D0

=

k =

(a)

What is its temperature (in °F) after 45 min? (Round your answer to the nearest whole number.)

°F

(b)

After how many hours will the turkey cool to 100°F? (Round your answer to one decimal place.)

hr

Answer 1

T(t) = 76 + (185 - 76)e^-kt = 76 + 109e^-kt

T(30) = 76 + 109e^-30k = 155

109e^-30k = 79

e^-30k = 0.7247706

-30k = ln(0.7247706)

k = 0.01073

T(t) = 76 + 109e^-0.01073t

(a). Find T(45)

(b). Solve for t if T(t) = 100 .