The rate of change of the population of a colony of bacteria is modelled by the function $\frac{dP}{dt} = 2t + 3e^{t}$, where $P$ is the population size and $t$ is the time in hours. Initially, at $t=0$, the population is 5.
a. Find the function $P(t)$ that represents the population size at time $t$.
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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 Anti-derivatives. It falls under Calculus 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 limits, continuity, differentiability, differentiation, and anti-differentiation.
anti-derivatives of polynomial functions and functions of the form $f(a x+b)$ where $f$ is $x^{n}$, for $n \in Q, e^{x}$, $\sin (x), \cos (x)$ and linear combinations of these
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