The temperature of a cup of coffee varies according to newton's law of cooling: , where t is the water temperature, a is the room temperature, and k is a positive constant.
if the coffee cools from 180°f to 100°f in 10 minutes at a room temperature of 75°f, how long (to the nearest minute) will it take the water to cool to 80°f?

Starting with:

T0 is initial temperature of coffee ---> 180
A = 75

Step 1: Find value for k
plug in T = 100, t = 10 min


This is just as good as finding an actual value for 'k' because it will be subbed into Cooling equation anyway. Subbing in e^(-k) is easier.

Step 2: Find value for 't' when T = 80


Therefore it takes about 21 minutes for coffee to cool from 180 to 80 degrees.

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