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.
📋 Examiner Report & Trap Analysis
Common mistake: 62% of candidates selected the distractor because they confused... The examiner specifically designed this question to test whether students can differentiate between... To secure full marks, candidates must demonstrate...
🎯 Mark Scheme Breakdown
Award 1 mark for identifying the correct principle. Award 1 mark for showing clear working. Common errors include failing to convert units and misreading the scale. The examiner report notes that only 34% of candidates achieved full marks on this question.
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