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. 483 questions covering 13.1 Integrating x^n, 13.2 Indefinite Integrals, 13.3 Finding Functions, 13.4 Definite Integrals, 13.5 Areas under Curves, 13.6 Areas under the x-axis, and 13.7 Areas between curves and lines, 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.
