Chloe' L.
asked • 03/07/21Exponential and Logarithmic Models
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?
(b) When will the turkey cool to 100∘ Fahrenheit?
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1 Expert Answer
The turkey's temperature will decrease according to Newton's Law of Cooling, a very common precalc and calculus formula that is an exponential decay function shifted up, so it has a horizontal asymptote of the surrounding (room) temperature.
t: time after turkey is removed from oven (in minutes)
T(t): temperature of turkey (in °F)
T(t) = 75 + 110e-kt Here 110 is the initial difference in temp between the turkey and room.
k is a constant that determines the rate of cooling, which we can solve for by using the given point: (30 , 154)
So conclude by plugging in 30 for t and 154 for T(30) and use natural logs to solve for k.
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Stanton D.
So Chloe' L., the cooling is exponential. The turkey temperature is decaying from initial (185F) towards equilibrium (75F). You have one timed data point to use to solve for the rate constant (k) in the exponential decay function. Then use that value for k to solve the rest of the given temperatures -> times. -- Cheers, --Mr. d. P.S. Great that you kept the accent aigu!03/07/21