The Math behind cooling down coffee

I'll try to put it down in general way what I'm going to right here is only basicly true and by no way should you use it at scool or universty. The heat of the coffe is actually the speed by wich the water molecule are traveling in the glass, the hotter the coffe the faster the molecules are moving, it's actullay molecular kinetyc energy. the cooling down of the coffe happens when the fast water molecule hits another molecule (of the air or the glass) and transfer part of it's enrgy and momentum to the other molecule. now cosider to cars, one is traveling 100 kmh and the second 60 kmh if I'll put an iron wall infront of them both the car will slow down to stop at about the same time so the fastest car loosed more energy at the same time. this is somewhat the same with the model I've reaten above of the coffe. as I said before, all I have writen above is based about the litle knowladge I know about phase transfer, and is not entairly true, it's only an easy way to look at it. tell us what alse you have found and sorry for my bad eanglish

Firstly, a cup of coffee at 100 degrees will take longer to get to 80 degrees than a cup of coffee that started at 90 degrees.  The "exponential" aspect is that when you look at the temperature over time, the temperature will decrease asymptotically to room temperature, meaning that as it gets closer to room temperature, the temperature will change more slowly.  This is due to the temperature difference between the coffee and the room (the temperature difference is the driving force of the exchange of energy).  So, that first degree from 100 to 99 will be "faster" than the temperature drop from 90 to 89.  There is no "acceleration" of the temperature change that gives advantage to starting out hotter.

The difference between "white" coffee and "black" coffee in terms of cooling effects is minimal.  Yes, black bodies radiate away more heat, but the reality of the situation is such that it is inconsequential to the heat capacity of the coffee cup, the exposed surface area, and the environment.  

But will it be better to add milk in five minutes, or should I add it now and wait five minutes?  Given the volumes and factors involved... IT DOESN'T MATTER.

listen to jackvinson his explanation is much better then mine

 I wanted to add the part you added at the end (about waiting or not before adding cream) but I couldn't find the right words.

if you want, every book about thermodynamics (physical chemistry) will have this part, it's related to enthory and heat capacities

The conclusion jackvinson made about when is better to add the milk is not that straight-forward. The right conclusion is that IT MATTERS (depending on where the milk is being kept ?!).

While the coffee is loosing temprature (i.e. being cooled) until finally reaching the room temprature, the milk is usually being kept in the refrigirator, which is cooler than the room temprature  (otherwise it would be used as a heater ). In that case, in some point of time the added cold milk will reducef the temprature of the coffe below the room temprature (and you'll then have to wait while it gain temprature until it finally reaches the room temprature). 

On the other hand, if the milk is added to the coffee in the beginning, the coffee's temprature will never drop below the room temprature. (this statement also has exception:  if the amount of cold milk is much more (e.g. 5X) than the amount of hot coffee)

Anyway, enjoy your coffee!