The rate of change of the temperature of a plastic mold (yyy) in a cooling chamber is directly proportional to the difference between the temperature of the mold and the chamber air (22∘C22^{\circ}\text{C}22∘C).
Write down a differential equation for this relationship.
Show that y=22+Aekty = 22 + Ae^{kt}y=22+Aekt where A A\,A and k k\,k are constants.
Given that the initial temperature of the plastic mold is 182∘C182^{\circ}\text{C}182∘C, write down the value of AAA.
After 12 minutes, the temperature of the mold is 62∘C62^{\circ}\text{C}62∘C. Show that k=−16ln2\displaystyle k = -\frac{1}{6} \ln 2k=−61ln2.
