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6 marksSequences

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

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.

Calculate the EXACT value of k and of r.

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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)(i)What is the LARGEST number reached by the membership of the club?[2 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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