A biologist is studying the growth of a bacterial colony in a petri dish. She observes that the growth pattern can be modeled using a combination of exponential and logarithmic functions. The temperature of the dish is also changing, affecting the growth rate.
a. Initially, the biologist models the bacterial population, $P(t)$, at time $t$ (in hours) with the function $P(t) = A e^{kt}$, where $A$ and $k$ are positive constants. She determines that at $t=0$, $P(0) = 1000$, and at $t=2$, $P(2) = 2500$. Determine the values of $A$ and $k$.
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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 Graphs of Power, Exponential, Log, Circular 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.
graphs of the following functions: power functions, $y=x^{n}, n \in Q$; exponential functions, $y=a^{x}, a \in R^{y}$, in particular $y=e^{x}$; logarithmic functions, $y=\log _{x}(x)$ and $y=\log _{(x)}(x)$; and circular functions, $y=\sin (x), y=\cos (x)$ and $y=\tan (x)$ and their key features
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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 Graphs of Power, Exponential, Log, Circular Functions.
