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11.11 Modelling with Differential Equations

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Question 29

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

\frac{\text{d}M}{\text{dt}} = \frac{M^{\frac{3}{2}}}{6t^2}, \quad t > 0

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

show that

\left( \frac{pt}{qt + r} \right)^2

where $p$ , $q$ , and $r$ are integers to be found.

[6]

According to the model, find the limiting value of the mass of the deposit as $\to \infty$ .

[2]

Markscheme

11.11 Modelling with Differential Equations Questions

A Level
Maths
11.11 Modelling with Differential Equations

50 exam-style questions on Edexcel A Level Maths 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

11.11 Modelling with Differential Equations

Question bank

11.11 Modelling with Differential Equations

Medium Hard

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Question 29

\frac{\text{d}M}{\text{dt}} = \frac{M^{\frac{3}{2}}}{6t^2}, \quad t > 0

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

show that

\left( \frac{pt}{qt + r} \right)^2

where $p$ , $q$ , and $r$ are integers to be found.

[6]

According to the model, find the limiting value of the mass of the deposit as $\to \infty$ .

[2]

Markscheme

11.11 Modelling with Differential Equations Questions

A Level
Maths
11.11 Modelling with Differential Equations

50 exam-style questions on Edexcel A Level Maths 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.