A biologist is studying the population growth of two species of bacteria, A and B, in a shared petri dish. The population of bacteria A at time $t$ (in hours) is modeled by the function $a(t) = 1000e^{0.2t}$, and the population of bacteria B is modeled by the function $b(t) = \frac{2000t}{1 + 0.1t}$.
Determine the rate of change of the total bacteria population in the petri dish when $t = 5$ hours. Express your answer to the nearest whole number.
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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 Derivatives of Combined Functions. 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.
derivatives of $f(x) \pm g(x), f(x) \times g(x), \frac{f(x)}{g(x)}$ and $(f \circ g)(x)$ where $f$ and $g$ are polynomial functions exponential, circular, logarithmic or power functions and transformations or simple combinations of these functions
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