A-LevelMathematicsDifferential equationsOct/Nov 2019Paper 3 Q48 Marks
The number of insects in a population t weeks after the start of observations is denoted by N. The population is decreasing at a rate proportional to Ne-0.02t. The variables N and t are treated as continuous, and it is given that when t = 0, N = 1000 and dN = -10. dt (i) Show that N and t satisfy the differential equation dN = -0.01e-0.02t N. dt (ii) Solve the differential equation and find the value of t when N = 800. (iii) State what happens to the value of N as t becomes large.
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