The rate of change of the temperature of a kettle of water (yyy) after it boils is directly proportional to the difference between the temperature of the water and the room temperature (20∘C20^{\circ}\text{C}20∘C).
Write down a differential equation for this relationship
Show that y=20+Aekty = 20 + Ae^{kt}y=20+Aekt where A A\,A and k k\,k are constants
Given that the initial temperature is 100∘C100^{\circ}\text{C}100∘C write down the value of AAA.
After 8 minutes the temperature is 60∘C60^{\circ}\text{C}60∘C show that k=−18ln2\displaystyle k = -\frac{1}{8} \ln 2k=−81ln2
