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 $t\geq 0$.
Marking your answer...
This may take a few seconds
Sign up for free to see your full marking breakdown and personalised study recommendations.
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 $\tan (x)$
All free, all instant AI marking.
State the derivative with respect to $x$ for each of the following functions: a. $f(x) = x^7$ b. $g(x) = e^{4x}$ c. $h(x) = \log_e(5x)$ d. $…
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) +…
StudyPulse has thousands of VCE Mathematical Methods questions with full AI feedback, mark breakdowns, progress tracking, and study notes across every Key Knowledge point including Derivatives of Basic Functions.
