The concentration of a chemical reactant in a solution, CCC mg/L, after ttt minutes is modeled by the equation:
log10C=1.84−0.072t \log_{10} C = 1.84 - 0.072t log10C=1.84−0.072tShow that this equation can be written in the form C=km−tC = km^{-t}C=km−t, where kkk and mmm are constants. Give the value of kkk to the nearest whole number and the value of mmm to 2 significant figures.
With reference to the equation in part (a), interpret the value of the constant kkk.
When the reaction temperature is increased, the concentration CCC after ttt minutes satisfies the equation:
C=560×1.15−t C = 560 \times 1.15^{-t} C=560×1.15−tUse calculus to find, to 2 significant figures, the value of dCdt\frac{dC}{dt}dtdC when t=4t = 4t=4.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, 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.
