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.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, 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). Each one has a worked solution and a mark scheme showing where the marks go.