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.
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.