A new social media platform, ‘ConnectU’, is experiencing rapid growth in its user base. The platform’s administrators are modelling the user growth to predict future server capacity needs and plan marketing strategies.
c. The administrators are also considering a piecewise function to model the user growth, defined as:
$$M(t) = \begin{cases}500e^{0.4479t}, & 0 \le t < 12 \ 15000 + 1863\ln(t-11), & 12 \le t \le 24\end{cases}$$
Describe the key features of this piecewise function, including its continuity at $t = 12$, and suggest one potential limitation of using this model to predict user growth beyond 24 weeks.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 4 marks, testing your understanding of Modelling with Functions. It falls under Functions, relations and graphs 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 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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