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4 marksIntegration

CAPE Integrated Mathematics · 2016 · Paper 2 · Question 6(c)(i)

The rate of increase of a population, P, at time t (in years) is proportional to the population P.

Show that P satisfies the equation P(t) = e^(kt + c).

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Other parts of this question

  1. 6(a)(i)Determine the integral: int (4x + 7)^6 dx.[3 marks]
  2. 6(a)(ii)Determine the integral: int (5x^3 - 3x^2 + 1) dx.[2 marks]
  3. 6(b)Evaluate the definite integral int_0^(pi/2) (cos x + 2 sin x) dx.[4 marks]
  4. 6(c)(ii)When t = 0, P = 4000. Calculate the value of c.[2 marks]
  5. 6(c)(iii)Given that k = ln 2, determine the population size when t = 3.[3 marks]
  6. 6(d)(i)Find the value of Q.[3 marks]
  7. 6(d)(ii)Using integration, determine the area reserved for agricultural activities. Give your answer to the nearest whole number.[4 marks]

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