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11.10 Solving Differential Equations

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Question 17

A beam of light travels through a container of murky liquid. The rate of change of the light's intensity, $I$ lux, with respect to the depth, $x$ metres, is modeled by the equation:

R = -0.75 I^2

where $R$ is the rate of change $dIdx\frac{dI}{dx}$ . The intensity of the light as it enters the liquid at the surface (where $x = 0$ ) is $4$ lux.

By first forming a suitable differential equation, show that

\frac{4}{3x + 1}

[4]

Determine the rate of change of the light's intensity with respect to depth when $x = 1$ .

[2]

Markscheme

11.10 Solving Differential Equations Questions

A Level
Maths
11.10 Solving Differential Equations

34 exam-style questions on Edexcel A Level Maths 11.10 Solving Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

11.10 Solving Differential Equations

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11.10 Solving Differential Equations

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Question 17

A beam of light travels through a container of murky liquid. The rate of change of the light's intensity, $I$ lux, with respect to the depth, $x$ metres, is modeled by the equation:

R = -0.75 I^2

where $R$ is the rate of change $dIdx\frac{dI}{dx}$ . The intensity of the light as it enters the liquid at the surface (where $x = 0$ ) is $4$ lux.

By first forming a suitable differential equation, show that

\frac{4}{3x + 1}

[4]

Determine the rate of change of the light's intensity with respect to depth when $x = 1$ .

[2]

Markscheme

11.10 Solving Differential Equations Questions

A Level
Maths
11.10 Solving Differential Equations

34 exam-style questions on Edexcel A Level Maths 11.10 Solving Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.