Mathematics (AS & A Level) · Oct / Nov 2016 · Paper 32 · Question 10

A large field of area 4 km2 is becoming infected with a soil disease. At time t years the area infected is x km2 and the rate of growth of the infected area is given by the differential equation dx dt = kx4 −x , where k is a positive constant. It is given that when t = 0, x = 0.4 and that when t = 2, x = 2. 1

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