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
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 100 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.