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

Question 1032285: 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 minute, how long does it take for the lemonade to cool to 55�F?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The DE becomes .
==> ln(T-38) = kt + c.
T(0) = 75 ==> ln37 = c. ==> .
Now T(30) = 60 ==> , or .
==> , or
==> , or
.
To solve for t when T = 55, plug 55 for T into the last equation.
I will leave the final calculation to you, and you should manage to get minutes, to the nearest minute.
RELATED QUESTIONS
Newton�s law of cooling states that the rate of cooling of an object is proportional to... (answered by robertb)

Newton�s law of cooling states that the rate of cooling of an object is proportional to... (answered by Fombitz)

Newton�s law of cooling states that the rate of cooling of an object is proportional to... (answered by Fombitz,robertb)

Newton�s law of cooling states that the rate of cooling of an object is proportional to... (answered by Fombitz)

newtons law of cooling states that the rate at which an object cool is directly... (answered by Boreal)