A researcher is studying the growth of a bioluminescent organism. The volume VVV of the organism (in mm3\text{mm}^3mm3) satisfies the differential equation
dVdt=6t2lntV \frac{\text{d}V}{\text{d}t} = \frac{6t^2 \ln t}{V} dtdV=V6t2lntfor t≥1t \ge 1t≥1, where ttt is the time in days since the start of the observation.
Given that the volume of the organism is 4 mm34\text{ mm}^34 mm3 when t=1t = 1t=1, solve the differential equation to find an expression for V2V^2V2 in terms of ttt.
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.
