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1.8 Exponentials and Logarithms

1.8 Exponentials and Logarithms

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Question 63

The concentration CCC (in mg/L) of a bioactive compound in a chemical reactor is modelled by the equation

C=pqt C = pq^t C=pqt

where ppp and qqq are constants and ttt is the time in hours since the reaction began.

The relationship between ttt and log⁡10C\log_{10} Clog10​C is linear. The graph of this relationship passes through the vertical intercept (0,1.48)(0, 1.48)(0,1.48) and the point (25,0.73)(25, 0.73)(25,0.73).

a.

Find an equation for this line in the form log⁡10C=mt+c\log_{10} C = mt + clog10​C=mt+c.

[2]
b.

Find the value of ppp and the value of qqq, giving your answers to 3 significant figures.

[2]
c.

According to the model, find the value of ttt when the concentration reaches 10 mg/L.

[2]
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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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