The population, $P$, of a species of endangered birds on a remote island is modeled by the equation $P(t) = rac{1000te^{-0.01t}}{1 + 0.1t}$, where $t$ is the time in years since the start of a conservation program.
a. Find an expression for $P’(t)$, the rate of change of the bird population with respect to time.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 marks, testing your understanding of Derivatives of Combined 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 $f(x) \pm g(x), f(x) \times g(x), \frac{f(x)}{g(x)}$ and $(f \circ g)(x)$ where $f$ and $g$ are polynomial functions exponential, circular, logarithmic or power functions and transformations or simple combinations of these functions
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State the derivative of the function $f(x) = e^{2x} + x^3 - \cos(x)$.
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The concentration, $C$ (in mg/L), of a drug in a patient's bloodstream is modeled by the function $C(t) = rac{5te^{-0.2t}}{1 + t}$, where $t…
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