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2 Unit AS 2: Applied Mathematics

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Question 233

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

2 Unit AS 2: Applied Mathematics Questions

  1. A Level
  2. /Maths
  3. /2 Unit AS 2: Applied Mathematics

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