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=−0.75I2where 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.
By first forming a suitable differential equation, show that
I=43x+1 I = \frac{4}{3x + 1} I=3x+14Determine the rate of change of the light's intensity with respect to depth when x=1x = 1x=1.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
