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WMA12/01 Jan 2020, Question 5: Solving Exponential and Log Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 8 marks

The question, in short

Geometric sequence model for a bee colony starting at 30000 and reaching 34000 after 3 years; find the annual percentage increase and the first year count exceeds 75000.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 3 marks

Find p, the annual percentage increase, to 2 decimal places, using the geometric sequence model.

  1. 130 000 × r³ = 34 000
  2. 2r³ = 17/15
  3. 3r = ∛(17/15) = 1.04260…
  4. 4p = 4.26

Answerp = 4.26

Part (b) · 5 marks

Find the smallest integer N for which the bee count exceeds 75000, showing all working.

  1. 130 000 × 1.0426ᴺ > 75 000
  2. 21.0426ᴺ > 5/2
  3. 3N log 1.0426 > log 2.5
  4. 4N > log 2.5 / log 1.0426 = 21.96
  5. 5Smallest integer N = 22

AnswerN = 22

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