A biologist is studying the population of rabbits on a small island. They observe that the population fluctuates seasonally. The population can be modelled using a combination of trigonometric and exponential functions.
a. The biologist initially models the rabbit population using the function $R(t) = 500 + 200\cos(\frac{\pi}{6}t)$, where $R(t)$ is the number of rabbits at time $t$ months. State the maximum and minimum rabbit population predicted by this model.
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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 Modelling with Functions. It falls under Functions, relations and graphs 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 transformations, polynomial functions, power functions, exponential functions, logarithmic functions, circular functions, and combinations of these.
modelling of practical situations using polynomial, power, circular, exponential and logarithmic functions, simple transformation and combinations of these functions, including simple piecewise (hybrid) functions.
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