Does anyone know how to work a Newton's Law of Cooling problem?

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 equals k times the quantity T minus 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?

Question

Does anyone know how to work a Newton's Law of Cooling problem? 

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 equals k times the quantity T minus 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?

tkhunny · Answer

What work have you done?

There is a temperature difference.
The change is proportional to that.
Set it up.

anonymous · Answer

Well, there are two parts to the question, I've done the second part already which asked how many minutes would it take for the lemonade to cool to 55 degrees. I figured out that it would take approx. 45 minutes and i could set that up fine, I'm just having trouble with the set up, I'm not asking for the answer

noelgreco · Answer

Did you calculate C and k?

noelgreco · Answer

$$T - T _{a}=Ce ^{kt}$$