The concentration, $C$ (in mg/L), of a drug in a patient’s bloodstream is modelled by $C(t) = rac{5t}{t^2 + 1}$, where $t$ is the time in hours since the drug was administered. A therapeutic effect is achieved when the concentration is above 2 mg/L. Determine the total duration, in hours, for which the drug concentration is within the therapeutic range. Justify your answer, showing all relevant working and reasoning.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 6 marks, testing your understanding of Solution of Equations f(x) = g(x). 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.
solution of equations of the form $f(x)=g(x)$ over a specified interval, where $f$ and $g$ are functions of the type specified in the 'Functions, relations and graphs' area of study, by graphical, numerical and algebraic methods, as applicable
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The population, $P$, of a bacterial colony at time $t$ hours is modelled by the equation $P = 100e^{0.5t}$. A competing bacterial colony has…
Consider the functions $f(x) = 2x - 1$ and $g(x) = 3$, where $x \in [-2, 5]$. State the solution to the equation $f(x) = g(x)$ within the sp…
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