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1.6 Exponentials and logarithms

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Question 52

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 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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