The concentration of a specific chemical pollutant in a local reservoir, C mg L−1C\text{ mg L}^{-1}C mg L−1, ttt hours after a purification process begins, is modeled by the equation
C=A+200e−λt C = A + 200e^{-\lambda t} C=A+200e−λtwhere AAA and λ\lambdaλ are positive constants. Given that the initial concentration of the pollutant is 215 mg L−1215\text{ mg L}^{-1}215 mg L−1,
find the value of AAA.
The concentration of the pollutant 6 hours after the purification process begins is 40 mg L−140\text{ mg L}^{-1}40 mg L−1.
Show that λ=plnq\lambda = p \ln qλ=plnq where ppp and qqq are rational numbers to be found.
Hence find
the concentration of the pollutant 12 hours after the process begins, giving your answer to 3 significant figures,
the rate of decrease of the concentration of the pollutant 12 hours after the process begins. Give your answer in mg L−1h−1\text{mg L}^{-1} \text{h}^{-1}mg L−1h−1 to 3 significant figures.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing 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.
