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1.8 Exponentials and Logarithms

1.8 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

1.8 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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