Newton’s law of cooling says that the rate at which an object cools is proportional to the difference between its temperature and that of its surroundings.
In other words, if f(t) is the temperature difference between the object and
its surroundings, taken at time t, then
f'(t) = kf(t) for some constant k:
A bucket of water is placed outdoors on a winter’s night when the temperature is a constant 20
Celsius. The temperature of the water is 30
Celsius
when it is first put out. After 20 minutes the temperature of the water has
dropped to 15
Celsius. How long will it take for the water to freeze? (Just
to avoid real world issues, you may assume the water is constantly being
stirred, so that its temperature is the same throughout.