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 AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
