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Question 640

A crystalline deposit of mass MMM milligrams is formed on an electrode during a chemical process. At time ttt seconds after the process begins, the rate of increase of the mass is modeled by the differential equation

dMdt=M326t2,t>0 \frac{\text{d}M}{\text{dt}} = \frac{M^{\frac{3}{2}}}{6t^2}, \quad t > 0 dtdM​=6t2M23​​,t>0

Given that M=16M = 16M=16 when t=4t = 4t=4,

a.

show that

M=(ptqt+r)2 M = \left( \frac{pt}{qt + r} \right)^2 M=(qt+rpt​)2

where ppp, qqq, and rrr are integers to be found.

[6]
b.

According to the model, find the limiting value of the mass of the deposit as t→∞t \to \inftyt→∞.

[2]
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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