# Question: a cup of hot coffee is initially 80 degrees celcius...

###### Question details

A cup of hot coffee is initially 80 degrees celcius and is left to stand in a room whose ambient temperature is 20 celcius. Suppose that at time t=0 the rate of coolong is 6 celcius per minute. i) assume that newton's law of cooling applies, the rate of cooling is proportional to the difference between the coffee's current temperature and the ambient temperature. Derive an equation that models the temperature of the coffee.

ii) how long does it take for the coffee to cool to a temperature 40 celcius?

iii) what is the limiting temperature of coffee at infinitely long times?