10 012 points I Previous Answers SPreCalc7 4.6.027.M My N This exercise uses New

Question

10 012 points I Previous Answers SPreCalc7 4.6.027.M My N 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 77°F (a) If the temperature of the turkey is 155°F after half an hour, what is its temperature after 45 min? (Round your answer to the nearest whole number.) 141 (b) After how many hours will the turkey cool to 100 ? (Round your answer to one decimal place.) hr Need Help? LRead it-j L watchi-L Watch It Master It

Explanation / Answer

Newton law of coolin' here :
T(t) = Ta + (Th - Ta)e^(-kt)

where,
T(t) = Temperature at time t,
TA = Ambient temperature (temp of surroundings),
TH = Temperature of hot object at time 0,
k = positive constant and
t = time.

T = 77 + (185 - 77)e^(-kt)

T = 77 + 108e^(-kt)

Now, T = 155 when t = 30 min :
155 = 77 + 108e^(-30k)
155 - 77 = 108e^(-30k)
78 = 108e^(-30k)
k = 0.010847

So, now
T = 77 + 108e^(-0.010847t)

After 45 min :
77 + 108e^(-0.010847*45)
143.2884866743072796

143 ---> ANS

-----------------------------------------------------------------

100 = 77 + 108e^(-0.010847t)

23/108 = e^(-0.010847t)

ln(23/108)= -0.010847t

t = 142.5866148423591777 min

So, after 142.5866148423591777/60,
i.e 2.4 hrs ---> ANS

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