A pharmaceutical company is developing a new drug. The concentration of the drug in a patient’s bloodstream is modeled by two functions. The concentration of the active ingredient entering the bloodstream is given by $f(t)$, and the rate at which the body metabolizes the drug is given by $g(c)$, where $t$ is time in hours and $c$ is the concentration of the drug.
a. The function $f(t) = 2t e^{-0.5t}$ models the concentration (in mg/L) of the drug entering the bloodstream over time (in hours). The function $g(c) = 0.1c^2$ models the rate (in mg/L per hour) at which the body metabolizes the drug at a given concentration $c$. Explain what the composite function $g(f(t))$ represents in this context and state its units.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 2 marks, testing your understanding of Composition of Functions. It falls under Algebra, number and structure 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 algebra of functions, inverse functions, and solutions of equations and systems of equations.
composition of functions, where $f$ composite $g, f \circ g$, is defined by $(f \circ g)(x)=f(g(x))$ given $r_{g} \subseteq d_{f}$
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