The population, $P$, of a particular species of insect in a controlled environment can be modelled by the function
$$P(t) = A e^{kt}$$,
where $t$ is the time in days, and $A$ and $k$ are positive constants. Initially, at $t = 0$, the population is 100.
After 7 days, the population has grown to 350.
a. Find the value of $A$ and $k$. Give the value of $k$ correct to four decimal places.
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 3 marks, testing your understanding of Inverse Functions. It falls under Algebra, number and structure 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 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.
The function $f(x) = rac{ae^{x}}{e^{x} + b}$, where $a$ and $b$ are positive real constants, has a horizontal asymptote at $y = 2$ and passe…
The function $f(x) = e^{2x} - 3$ is defined for the domain $x \in [0, a]$, where $a > 0$. Find the largest possible value of $a$ such that t…
State the condition that must be satisfied for a function $f(x)$ to have an inverse function, $f^{-1}(x)$. Give an example of a function tha…
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.
