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.
425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.