The concentration, CCC mg/L, of a chemical catalyst in a bio-reactor, ttt hours after the reaction begins, is modeled by the equation
C=L+240e−rt C = L + 240e^{-rt} C=L+240e−rtwhere LLL and rrr are positive constants. Given that the initial concentration of the catalyst is 275275275 mg/L,
find the value of LLL.
The concentration of the catalyst 5 hours after the reaction begins is 110110110 mg/L.
Show that r=plnqr = p \ln qr=plnq where ppp and qqq are rational numbers to be found.
Hence find
the concentration of the catalyst 10 hours after the reaction begins, giving your answer to 3 significant figures,
the rate of decrease of the concentration of the catalyst 10 hours after the reaction begins. Give your answer in mg/L h−1\text{mg/L h}^{-1}mg/L h−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.
