An ecologist is monitoring two distinct populations of insects.
The number of insects, NNN, in the first population is modelled by the equation
N=Aekt,t≥0 N = A e^{kt}, \quad t \ge 0 N=Aekt,t≥0where A A\,A and k k\,k are positive constants and t t\,t is the time in days from the start of the observation.
Given that:
Find the exact value of A A\,A and the value of k k\,k to 4 significant figures.
The number of insects, NNN, in the second population is modelled by the equation
N=80000e−0.4t,t≥0 N = 80000 e^{-0.4t}, \quad t \ge 0 N=80000e−0.4t,t≥0where t t\,t is the time in days from the start of the observation.
Find the rate of decrease of insects in this second population exactly 4 days from the start. Give your answer to 3 significant figures.
When t=Tt = Tt=T, the number of insects in the two populations was the same.
Find the value of TTT, giving your answer to 3 significant figures.
(Solutions relying entirely on calculator technology are not acceptable.)
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
