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1.6 Exponentials and logarithms

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Question 44

A chemical engineer is studying the rate at which a specific solid reactant dissolves in a solvent. The mass of the remaining reactant, MMM grams, is recorded hhh hours after the process begins. The relationship is modelled by the equation

log⁡10M=−0.0583h+1.9030≤h≤24 \log_{10} M = -0.0583h + 1.903 \quad 0 \le h \le 24 log10​M=−0.0583h+1.9030≤h≤24
a.

Show that this equation may be written in the form

M=abh M = ab^h M=abh

where aaa and bbb are constants to be determined. Give the value of aaa to the nearest integer and give the value of bbb to 3 significant figures.

[4]
b.

Use the model to predict the mass of the reactant remaining after 24 hours. Give your answer to 2 significant figures.

[2]
Markscheme

1.6 Exponentials and logarithms Questions

  1. A Level
  2. /Maths
  3. /1.6 Exponentials and logarithms

104 exam-style questions on WJEC A Level Maths 1.6 Exponentials and logarithms, covering 1.6.1 Exponentials and logarithms, 1.6.2 Exponentials and logarithms, 1.6.3 Exponentials and logarithms, 1.6.4 Exponentials and logarithms, 1.6.5 Exponentials and logarithms, 1.6.6 Exponentials and logarithms, 1.6.7 Exponentials and logarithms, 1.6.8 Exponentials and logarithms, and 1.6.9 Exponentials and logarithms. Each one has a worked solution and a mark scheme showing where the marks go.

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