In a controlled chemical synthesis, the rate of production of a particular polymer, R kg h−1R\text{ kg h}^{-1}R kg h−1, is modelled by the equation:
R=20.4−20.0e−0.5t−0.4e0.25t R = 20.4 - 20.0e^{-0.5t} - 0.4e^{0.25t} R=20.4−20.0e−0.5t−0.4e0.25twhere ttt is the time in hours since the reaction vessel was activated.
Determine the maximum production rate predicted by the model, giving your answer to one decimal place. Fully justify your answer.
Derive an expression for the total mass of polymer produced, M kgM\text{ kg}M kg, in terms of ttt.
After 15 hours, the total mass of polymer produced was measured to be 200 kg. Comment on the accuracy of the model.
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.
