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1.6 Exponentials and logarithms

1.6 Exponentials and logarithms

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Question 54

An environmental engineer is monitoring the concentration of a specific organic compound, CCC mg/L, in a testing chamber. The concentration ddd days after the start of the observation is modelled by the equation

C=pqd C = pq^d C=pqd

where ppp and qqq are positive constants.

A graph shows a linear relationship between log⁡10C\log_{10} Clog10​C and ddd. The line passes through the points (0,0.85)(0, 0.85)(0,0.85) and (12,1.45)(12, 1.45)(12,1.45).

a.

Find, to 3 decimal places, the value of ppp and the value of qqq.

[4]
b.

Using the model with the values found in part (a), find the rate of increase of the concentration of the compound, in mg/L per day, exactly 8 days after the start of the study. Give your answer to 2 decimal places.

[3]
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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