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1.11.7 Differential equations with separable variables (A-level only)

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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, III lux, with respect to the depth, xxx metres, is modeled by the equation:

R=−0.75I2 R = -0.75 I^2 R=−0.75I2

where RRR is the rate of change dIdx\frac{dI}{dx}dxdI​. The intensity of the light as it enters the liquid at the surface (where x=0x = 0x=0) is 444 lux.

a.

By first forming a suitable differential equation, show that

I=43x+1 I = \frac{4}{3x + 1} I=3x+14​
[4]
b.

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

[2]

1.11.7 Differential equations with separable variables (A-level only) Questions

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  3. /1.11.7 Differential equations with separable variables (A-level only)