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Newton’s law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. So the rate of cooling for a bottle of lemonade at a room temperature of 75°F which is placed into a refrigerator with temperature of 38°F can be modeled by dT/dt=k(T-38) where T(t) is the temperature of the lemonade after t minutes and T(0) = 75. After 30 minutes the lemonade has cooled to 60°F, so T(30) = 60. To the nearest degree, identify the temperature of the lemonade after an additional 30 minutes.

Respuesta :

scme1702
After the first 30 minutes,
dT = 75-60
= 15
dt = 30 mins
k = (15/60) * (60 - 38)
k = 5.5
After 60 minutes,
dT = 60 - T
dt = 30
(60 - T)/30 = 5.5(T - 38)
60 - T = 165T - 6270
166T = 6330
T = 38.13°F

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