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2 marksSequences

CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2 · Question 1(b)(i)

The enrolment pattern of membership of a country club follows an exponential logistic function N, where N = 800 / (1 + k e^(-r t)), k in R, r in R, where N is the number of members enrolled t years after the formation of the club. The initial membership was 50 persons and after one year, there are 200 persons enrolled in the club.

What is the LARGEST number reached by the membership of the club?

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Other parts of this question

  1. 1(a)(i)Show that f'(x) = x^2 ln x (3 ln x + 2).[5 marks]
  2. 1(a)(ii)Show that f''(x) = 6x ln^2 x + 10x ln x + 2x.[5 marks]
  3. 1(b)(ii)Calculate the EXACT value of k and of r.[6 marks]
  4. 1(b)(iii)How many members will there be in the club 3 years after its formation?[2 marks]

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