SOLUTION: 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 f

Algebra ->  Finance -> SOLUTION: 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 f      Log On


   

Question 1032278: 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, what is the temperature of the lemonade after an additional 30 minutes?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
This is just a follow-up to the other problem.
After 30 minutes, the temperature was 60°F.
After an additional 30 minutes, the temperature is T(60).
The equation that was obtained previously was T%28t%29+=+38%2B37%2822%2F37%29%5E%28t%2F30%29.
==> T%2860%29+=+38%2B37%2822%2F37%29%5E%2860%2F30%29+=+38%2B37%2822%2F37%29%5E2%7D+= 51°F, to the nearest degree.