The population, $P$, of a certain species of endangered bird is modelled by the differential equation $\frac{dP}{dt} = kP^{0.75} \cos(0.1t)$, where $t$ is measured in years and $k$ is a positive constant. At time $t = 0$, the population is 1000.
Given that the population reaches a maximum at $t = 5\pi$ years, determine the value of $k$.
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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 Derivatives of Basic Functions. 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.
derivatives of $x^{\mathrm{n}}$ for $n \in Q, \varepsilon^{k}, \log _{e}(x), \sin (x), \cos (x)$ and $\tan (x)$
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