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 AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
