# Differential Equation - Newton's Law Of Cooling?

• May 20th 2009, 05:04 PM
xvaliant
Differential Equation - Newton's Law Of Cooling?
I have a homework problem I'm not sure about.

At 6:00 pm a 50 degree drink is pulled from the refrigerator into a room that is 72 degrees. Three minutes later, at 6:03, the drink is now 53 degrees. How long, in minutes, will it be until the drink is 70 degrees?
• May 20th 2009, 05:43 PM
skeeter
Quote:

Originally Posted by xvaliant
I have a homework problem I'm not sure about.

At 6:00 pm a 50 degree drink is pulled from the refrigerator into a room that is 72 degrees. Three minutes later, at 6:03, the drink is now 53 degrees. How long, in minutes, will it be until the drink is 70 degrees?

$\frac{dT}{dt} = k(72 - T)$

$T(0) = 50$

$T(3) = 53$

solve the differential equation using the given conditions.
• May 20th 2009, 05:53 PM
xvaliant
ok, I integrated both sides an got ln(72-T)=kt. I'm confused as how to find the constant, k.
• May 20th 2009, 06:14 PM
skeeter
Quote:

Originally Posted by xvaliant
ok, I integrated both sides an got ln(72-T)=kt. I'm confused as how to find the constant, k.

where is your constant of integration?
• May 20th 2009, 06:21 PM
xvaliant
(72-T)=C(1) e^kt
• May 20th 2009, 06:37 PM
skeeter
Quote:

Originally Posted by xvaliant
(72-T)=C(1) e^kt

use $T(0) = 50$ to find $C_1$

use $T(3) = 53$ to find $k$
• May 20th 2009, 07:13 PM
xvaliant
Got it. Thanks!