The height, \(h\) meters, of a weather balloon above ground level can be modelled as a function of time, \(t\) minutes, after its release. Assume the balloon is released from ground level. The rate of change of the height of the balloon with respect to time is given by \(\frac{dh}{dt} = 3t^2 e^{-0.1t} + 2\), for \(t \geq 0\).
b. Explain why the rate of change of the height of the balloon, \(\frac{dh}{dt}\), is always positive for \(t\geq 0\).
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 2 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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