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1.8 Exponentials and Logarithms

1.8 Exponentials and Logarithms

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Question 56

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

1.8 Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /1.8 Exponentials and Logarithms

104 exam-style questions on OCR (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.

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