The rate of change of the temperature of a bowl of soup (SSS) cooling on a table is directly proportional to the difference between the temperature of the soup and the temperature of the room (18∘C18^{\circ}\text{C}18∘C).
Write down a differential equation for this relationship.
Show that S=18+AektS = 18 + Ae^{kt}S=18+Aekt where A A\,A and k k\,k are constants.
Given that the initial temperature of the soup is 98∘C98^{\circ}\text{C}98∘C, write down the value of AAA.
After 5 minutes, the temperature of the soup is 58∘C58^{\circ}\text{C}58∘C. Show that k=−15ln2\displaystyle k = -\frac{1}{5} \ln 2k=−51ln2.
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.