The number of squirrels, $S$, in a newly established suburban habitat is modelled by the function $S(t) = 5 + rac{45t}{t^2 + 9}$, where $t$ is the time in months since the habitat was established. A local council decides to introduce a population of predatory birds. The number of these birds, $B$, is modelled by $B(t) = rac{t}{5}$, where $t$ is the time in months since the habitat was established.
Analyse the long-term impact of the predatory birds on the squirrel population by determining the times when the number of squirrels equals the number of birds. Justify your answer by discussing the behaviour of both populations as $t$ increases without bound.
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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 Solution of Equations f(x) = g(x). It falls under Algebra, number and structure in Unit 4: Mathematical Methods Unit 4. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Continues the study of functions, algebra, calculus, and introduces probability and statistics.
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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Consider the functions $f(x) = x^3 - 6x^2 + 5x + 12$ and $g(x) = -x^2 + 5x + 6$. Determine the $x$-values for which $f(x) = g(x)$ over the i…
The graphs of $f(x) = x + 1$ and $g(x) = 5 - x$ are shown below for $x \in [-1, 5]$. State the $x$-value for which $f(x) = g(x)$.
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