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1.6 Exponentials and Logarithms

1.6 Exponentials and Logarithms

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Question 65

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]
Markscheme

1.6 Exponentials and Logarithms Questions

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

104 exam-style questions on OCR A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.

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