(a) Solve 2log3 x - log3(x + 6) = 1.
(b) Solve 52x+1 = 3x, giving your answer correct to 3 significant figures.
From Paper 1: Pure Mathematics
1111 marks
The number of fish, P, in a lake t years after stocking is modelled by P = 2000/(1 + 9e-0.4t).
(a) Find the initial number of fish.
(b) State the long-term number of fish predicted by the model.
(c) Find the time taken for the population to reach 1000.
(d) Show that dP/dt = 0.4P (1 - P/2000 ).
(e) Hence find the greatest rate of increase of the population.
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Exponentials and logarithms Exam Questions: OCR A-Level Maths | Plasmo