# Thread: Differential Equation - Newton's Law Of Cooling?

1. ## 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?

2. 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.

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

4. 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?

5. (72-T)=C(1) e^kt

6. Originally Posted by xvaliant
(72-T)=C(1) e^kt
use $T(0) = 50$ to find $C_1$

use $T(3) = 53$ to find $k$

7. Got it. Thanks!