How to use Newton's Law of Cooling to determine the time that will elapse before coffee reaches a certain temperature?

Question

anonymous · Answer

Newton's law of cooling$$\frac{ du }{ dt } = -k(u-T)$$

anonymous · Answer

The equation that we are working with is $$T(t) = T _{a} + (T _{o} - T _{a})e$$ for Newton's Law of cooling. The particular problem says that a cup of 210F coffee is placed on a table in a room that is 68F, and 10 minutes later, it is 200F. I need to use the above equation to determine how long it will be before the coffee cools to 180F.

I know that I'll need to plug these values in, but I am not sure which variables stand for which values.

anonymous · Answer

Haha sorry. I thought that was from differential equations. But i sure can help you.