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WMA12/01 Jun 2024, Question 10: Geometric Sequences in Context

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

The question, in short

Model dormice growing 3% yearly from 2000 and voles as a geometric sequence from two data points; find dormice after 6 years, the vole model N = abᵗ, and the time T when both populations are equal.

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

Part (a) · 2 marks

Using a geometric sequence starting at 2000 with 3% yearly increase, find the dormice count after 6 years, to 3 significant figures.

  1. 1Number after 6 years = 2000 × 1.03⁶
  2. 2= 2388.1… ≈ 2390

Answer2390

Part (b) · 3 marks

From 3690 voles at 4 years and 3470 at 7 years, find constants a and b in N = abᵗ, each to 2 significant figures.

  1. 13690 = ab⁴ and 3470 = ab⁷
  2. 2Divide: b³ = 3470/3690, so b = 0.9797… ≈ 0.98
  3. 3a = 3690 / 0.9797…⁴ = 4005… ≈ 4000
  4. 4N = 4000 × 0.98ᵗ

AnswerN = 4000 × 0.98ᵗ

Part (c) · 3 marks

Find T, to one decimal place, when the dormice number equals the vole number according to both models.

  1. 12000 × 1.03ᵀ = 4000 × 0.98ᵀ
  2. 2(1.03/0.98)ᵀ = 2
  3. 3T log(1.03/0.98) = log 2
  4. 4T = log 2 / log(1.03/0.98) = 13.9

AnswerT = 13.9

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