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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions 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), matched to the AQA A Level Maths (7357) 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.
