An environmental scientist is tracking the mass of substances in a filtration tank.
The mass, MMM, in milligrams, of a purifying bacteria culture is modelled by the equation
M=Aekt,t≥0 M = A e^{kt}, \quad t \ge 0 M=Aekt,t≥0where A A\,A and k k\,k are positive constants and t t\,t is the time in hours since the bacteria were introduced.
Given that:
Find the exact value of A A\,A and the value of k k\,k correct to 4 significant figures.
The mass, MMM, of a specific contaminant in the tank is modelled by the equation
M=12000e−0.15t,t≥0 M = 12000 e^{-0.15t}, \quad t \ge 0 M=12000e−0.15t,t≥0where t t\,t is the time in hours since the start of the filtration process.
Find the rate of decrease of the mass of the contaminant exactly 5 hours after the start. Give your answer in mg per hour to 3 significant figures.
At time t=Tt = Tt=T, the mass of the bacteria culture is equal to the mass of the contaminant.
Find the value of TTT, giving your answer to 3 significant figures.
(Solutions relying entirely on calculator technology are not acceptable.)
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.
