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 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.
