A high-altitude atmospheric research probe is launched to monitor the concentration, GGG, of a specific reactive trace gas. The rate of change of the concentration with respect to time ttt (in hours) is modeled by the differential equation
dGdt=G(16−2t)50,t≥0 \frac{dG}{dt} = \frac{G(16 - 2t)}{50}, \quad t \ge 0 dtdG=50G(16−2t),t≥0where G0G_0G0 is the initial concentration at the moment of launch (t=0t = 0t=0).
Show that the concentration is given by
G=G0e150(16t−t2)for 0≤t≤c G = G_0 e^{\frac{1}{50}(16t - t^2)} \quad \text{for } 0 \le t \le c G=G0e501(16t−t2)for 0≤t≤cwhere ccc is a constant to be found.
Find the exact maximum concentration of the gas recorded by the probe in terms of G0G_0G0. Fully justify your answer.
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.
