Newtons Law of Cooling

[rkbrock22]

Suppose that the temperature of a pan of warm water obeys Newton's law of cooling. The water (

C ) was put in a cooler and 10 minutes later the water's temperature was

C. After another 10 minutes, the temperature of the water was

C.
What was the temperature in the cooler?

I understand how to set this up, but I just can't seem to get it to work out... I have no clue what to do.

 

[Deleted member 4993]

Suppose that the temperature of a pan of warm water obeys Newton's law of cooling. The water (

C ) was put in a cooler and 10 minutes later the water's temperature was

C. After another 10 minutes, the temperature of the water was

C.
What was the temperature in the cooler?

I understand how to set this up, but I just can't seem to get it to work out... I have no clue what to do.

So set it up - and we will go from there....

 

[galactus]

If you know how to set it up, then use the initial conditions to solve for \(\displaystyle T_{m}\) in

\(\displaystyle \frac{dT}{dt}=k(T-T_{m})\)

\(\displaystyle T(0)=49, \;\ T(10)=42, \;\ T(20)=36\)

Solve the DE and then use the IC's to find \(\displaystyle k\) and then \(\displaystyle T_{m}\)