Consider a population $P(t)$ of a certain species at time $t$ (in years) modeled by the equation $P(t) = A e^{kt}$, where $A$ and $k$ are positive constants. Suppose scientists introduce a predator species whose consumption rate of the original species depends on the logarithm of the population. After introducing the predator, the population is now modeled by $$P’(t) = A e^{kt} - b \cdot \ln(P(t))$$, where $b$ is a positive constant.
Given that $A = e^{10}$, $k = \ln(2)$, and $b = 10$, determine the value of $t$ for which $P’(t) = 0$. Interpret your result in the context of the population model.
Marking your answer...
This may take a few seconds
Sign up for free to see your full marking breakdown and personalised study recommendations.
Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 5 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
All free, all instant AI marking.
StudyPulse has thousands of VCE Mathematical Methods questions with full AI feedback, mark breakdowns, progress tracking, and study notes across every Key Knowledge point including Inverse Functions.
