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3.5 Differentiation (A-level only)

3.5 Differentiation (A-level only)

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Question 116

The concentration of a chemical reactant in a solution, CCC mg/L, after ttt minutes is modeled by the equation:

log⁡10C=1.84−0.072t \log_{10} C = 1.84 - 0.072t log10​C=1.84−0.072t
a.

Show 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.

[3]
b.

With reference to the equation in part (a), interpret the value of the constant kkk.

[1]
c.

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−t

Use calculus to find, to 2 significant figures, the value of dCdt\frac{dC}{dt}dtdC​ when t=4t = 4t=4.

[3]
Markscheme

3.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Differentiation (A-level only)

263 exam-style questions on CCEA A Level Maths 3.5 Differentiation (A-level only), covering 3.5.1 Differentiation (A-level only), 3.5.2 Differentiation (A-level only), 3.5.3 Differentiation (A-level only), 3.5.4 Differentiation (A-level only), 3.5.5 Differentiation (A-level only), and 3.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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