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Question

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 145 Fahrenheit after half an hour, what is its temperature after 45 minutes?

   Fahrenheit

(b) When will the turkey cool to 100 Fahrenheit? 

   hours.

Answer 1

T(0.5) = 75 + (185 - 75)e^{- 0.5r} = 145; e^{- 0.5r} = 70/110; r = ln(7/11)/(- 0.5) = 0.904 h^-1.

(a) T(0.75) = 75 + (185 - 75)e^{- 0.75(0.904)} = 130,84 F

(b) 100 = 75 + 110e^{- 0.904t}; e^{- 0.904t} = 25/110; t = ln(25/110)/(-0.904) = 1.639 h