The population, $P$, of a newly discovered species of insect on a remote island is modelled by the equation
$$P(t) = 1000 + 500 \cos(0.5t) + 10t$$,
where $t$ is the time in weeks since the species was first observed.
Find the rate of change of the population with respect to time when $t = \frac{\pi}{2}$, and explain what this value represents in the context of the problem.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 4 marks, testing your understanding of Derivatives of Basic Functions. It falls under Calculus in Unit 4: Mathematical Methods Unit 4. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Continues the study of functions, algebra, calculus, and introduces probability and statistics.
Covers graphical treatment of limits, continuity and differentiability of functions of a single real variable, and differentiation, anti-differentiation and integration of these functions. This material is to be linked to applications in practical situations.
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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