The rate of change of the temperature of a bowl of soup (SSS) cooling on a table is directly proportional to the difference between the temperature of the soup and the temperature of the room (18∘C18^{\circ}\text{C}18∘C).
Write down a differential equation for this relationship.
Show that S=18+AektS = 18 + Ae^{kt}S=18+Aekt where A A\,A and k k\,k are constants.
Given that the initial temperature of the soup is 98∘C98^{\circ}\text{C}98∘C, write down the value of AAA.
After 5 minutes, the temperature of the soup is 58∘C58^{\circ}\text{C}58∘C. Show that k=−15ln2\displaystyle k = -\frac{1}{5} \ln 2k=−51ln2.