Fit Newton cooling using the temperature excess

[Newton’s Law of Cooling]

The rate of temperature loss is proportional to the difference between a body and its surroundings. Express this as a differential equation, using t for time and theta for body temperature.

A rod is immersed in water held at 15°C. It cools from 60°C to 40°C in 3 minutes. Find (i) its temperature at time t, and (ii) its temperature immediately after 9 minutes.