A scientist is studying the population of a particular species of insect in a controlled environment. The population, $N(t)$, at time $t$ (in days) is modeled by a function involving both exponential growth and a limiting factor. The scientist also needs to analyze the inverse of this population model to predict when the population will reach certain levels.
c. The scientist wants to determine how long it will take for the insect population to reach 120. Using the inverse function $t(N)$ obtained in part (a), calculate the time $t$ when $N(t) = 120$. Give your answer correct to two decimal places. Then, analyse the limitations of using this model to predict the insect population over a very long period (e.g., several years).
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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 Inverse Functions. 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.
functions and their inverses, including conditions for the existence of an inverse function, and use of inverse functions to solve equations involving exponential, logarithmic, circular and power functions
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