# Maths: A Cup of Coffee Anyone??? :)

Hey Guys,

It's that time of the term again when all exams are popping up!!
I'm just wondering if you'd be able to help me with this maths question that I'm a bit stuck on.

What we have to basically do is find out whether a cup of coffee will stay hotter longer when the milk is poured in first, or when it's poured in after the hot water. Our teacher isn't too fussy on which option we got out in the end, he is just interested in the steps we took to come to that conclusion.

Anyway, I have recorded the temperature over a period of time for each coffee ie. (milk in first, and milk in last).
By using Newton's Law of Cooling (which we were required to use), I have found the equations for T(t) where T=temperature and t=time, for both the coffees.

I am now just wondering how do I show which coffee type decreases at a faster rate??
Any help will be greatly appreciated.

Thanks for your time.
Chantelle.

ouldn't it depend on the room temperature, and the initial temperature of the creame? And whether if you mixed last, is the creame now warmed up by room temperature, or is it at the same intial temp from the fridge?

http://www.mast.queensu.ca/~peter/investigations/18coffeecream.pdf

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