A chemical spill pollutes a local reservoir. The concentration of the pollutant, $C(t)$ (in parts per million, ppm), at time $t$ (in days) after the initial spill is modelled by the function $$C(t) = 15e^{-0.1t} - 5e^{-0.2t}$$. Local authorities are using an environmental cleanup process to reduce the pollutants.
c. The local authorities claim that after 20 days, the total amount of pollutant removed is given by $\int_{0}^{20} C(t) dt$. Explain whether this integral represents the total amount of pollutant removed. If not, suggest a more appropriate integral to represent the total amount removed, assuming the cleanup process removes pollutant at a rate proportional to the concentration.
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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 Properties of Integrals. 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.
properties of anti-derivatives and definite integrals
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