A water tank is being filled such that the rate of change of its volume, $V$ (in litres), with respect to time, $t$ (in minutes), is given by $\frac{dV}{dt} = 5te^{-0.1t}$. Initially, the tank is empty. Determine the time at which the average volume of water in the tank from $t=0$ to that time is equal to half the instantaneous volume at that time. Give your answer correct to three decimal places.
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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 Application of intergration. 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.
application of integration to problems involving finding a function from a known rate of change given a boundary condition, calculation of the area of a region under a curve and simple cases of areas between curves, average value of a function and other situations.
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