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.
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.