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 Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, 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.
