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WMA12/01 Oct 2019, Question 2: Geometric Sequences in Context

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks

The question, in short

Model adult population growing 2% yearly from 25000 at start of 2019; find population at start of 2032 and total charity money from 2019 to 2032 inclusive at £5 per adult, rounded to nearest £1000.

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

Part (a) · 3 marks

Find the adult population at the start of 2032 using the geometric model with 25000 initial adults and 2% annual increase.

  1. 1Common ratio r = 1.02
  2. 22032 is 13 years after 2019, so use 13 increases
  3. 325000 × 1.02¹³ = 32340.2…
  4. 4Population ≈ 32 340

Answer32 340 (accept 32 341 or 32 300)

Part (b) · 3 marks

Find total charity money from 2019 to 2032 inclusive, with each adult giving £5 yearly, to nearest £1000.

  1. 12019 to 2032 inclusive is 14 years
  2. 2Total adults over 14 years: S₁₄ = 25000(1.02¹⁴ − 1)/(1.02 − 1) = 399 348.5…
  3. 3Money = 5 × 399 348.5… = 1 996 742.3…
  4. 4To the nearest £1000: £1 997 000

Answer£1 997 000

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Also searched as: WMA12 October 2019 · WMA12/01 · wma12 oct19 · IAS Maths Pure Mathematics 2 October 2019 · question 2.
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