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Question 307

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 (25∘C25^\circ\text{C}25∘C).

a.

Write down a differential equation for this relationship

[3]
b.

Show that y=25+Aekty = 25 + Ae^{kt}y=25+Aekt where A A\,A and k k\,k are constants, and hence, given that the initial temperature is 100∘C100^\circ\text{C}100∘C, find the value of AAA.

[5]
c.

After 10 minutes the temperature is 55∘C55^\circ\text{C}55∘C show that k=−110ln⁡52\displaystyle k = -\frac{1}{10}\ln\frac{5}{2}k=−101​ln25​

[3]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

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.

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