# Math Help - Differential Equations Word Problem...

1. ## Differential Equations Word Problem...

I think this one has to do with Newton's Law of Cooling, but here it is:

A red wine is brought up from the wine cellar, which is a cool 10 degrees Celsius, and left to breathe at room temperature 23 degrees Celsius. If it takes 10 minutes for the wine to reach 15 degrees Celsius, when will the temperature of the wine reach 18 degrees Celsius?

2. $\frac{dT}{dt} = k(23 - T)$ , $T(0) = 10$ , $T(10) = 15$

separate variables, integrate, and use your given values to determine k and the constant of integration.