The rate of change of the temperature of a heated metal rod (TTT) in a laboratory setting is directly proportional to the difference between the temperature of the rod and the constant room temperature (15∘C15^{\circ}\text{C}15∘C).
Write down a differential equation for this relationship.
Show that T=15+AektT = 15 + Ae^{kt}T=15+Aekt where A A\,A and k k\,k are constants.
Given that the initial temperature of the rod is 115∘C115^{\circ}\text{C}115∘C, write down the value of AAA.
After 10 minutes, the temperature of the rod is 65∘C65^{\circ}\text{C}65∘C. Show that k=−110ln2\displaystyle k = -\frac{1}{10} \ln 2k=−101ln2.
