The population of a newly discovered species of bacteria in a petri dish is modeled by a combination of exponential and logarithmic functions. The population, $P(t)$, in thousands, at time $t$ hours after the bacteria was introduced, is given by $$P(t) = A e^{kt} + B \log_2(t+1)$$, where $A$, $B$, and $k$ are positive constants.
b. Suppose it is known that $k = \ln(1.5)$. Determine the value of $B$. Then, describe the long-term behavior of the population as $t$ increases without bound, accounting for the contributions of both the exponential and logarithmic terms.
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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 Graphs of Power, Exponential, Log, Circular 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.
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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