A researcher is studying the rate of growth of a bacterial colony. They model the rate of growth by the function $f(t) = ae^{-kt}$, where $t$ is the time in hours, and $a$ and $k$ are positive constants. At time $t = 0$, the rate of growth is observed to be 1000 bacteria per hour. After 1 hour, the rate of growth has decreased to 500 bacteria per hour.
Using the properties of definite integrals, determine the total bacterial growth during the first 3 hours. Express your answer in terms of $e$.
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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 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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