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1.6 Exponentials and Logarithms

1.6 Exponentials and Logarithms

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Question 73

The amount of a specific bacteria in a culture, BBB, is modelled by the formula

B=pqt B = pq^t B=pqt

where ppp and qqq are constants and ttt is the number of hours after the measurement began at 12:00 PM. A graph of log⁡10B\log_{10} Blog10​B against ttt is plotted based on data from the first 4 hours. The data points follow a straight line with a gradient of 0.12 and a vertical intercept on the log⁡10B\log_{10} Blog10​B axis of 1.45.

a.

Determine the value of ppp and the value of qqq according to the model, rounding your answers to two decimal places.

[4]
b.

Provide a practical interpretation of the constant ppp in the context of this model.

[1]
c.

Use the model to estimate the bacteria count at 8:00 PM on the same day.

[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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