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.
b. After some time, the biologist observes that the rabbit population is decreasing exponentially due to a disease. They refine the model to include an exponential decay factor: $R(t) = (500 + 200\cos(\frac{\pi}{6}t))e^{-0.02t}$. Describe how the graph of $R(t) = 500 + 200\cos(\frac{\pi}{6}t)$ is transformed by the inclusion of the exponential factor $e^{-0.02t}$.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 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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