The population growth rate of a newly discovered insect species on a remote island is modeled by the function $\frac{dN}{dt} = 0.01N(100 - N) - h$, where $N(t)$ is the population size at time $t$ (in weeks) and $h$ represents the constant harvesting rate of insects by researchers for study purposes. Initially, the population is $N(0) = 200$.
a. With a harvesting rate of $h=50$, determine the population size $N(t)$ as a function of time $t$.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 5 marks, testing your understanding of Application of intergration. It falls under Calculus in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers limits, continuity, differentiability, differentiation, and anti-differentiation.
application of integration to problems involving finding a function from a known rate of change given a boundary condition, calculation of the area of a region under a curve and simple cases of areas between curves, average value of a function and other situations.
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