A biologist is studying the growth of a bacterial colony. She models the number of bacteria, $N(t)$, at time $t$ hours using different functions. For each of the following models, you are asked to find the rate of change of the bacterial population at a specific time.
c. If $N(t) = 1000\log_e(t+1)$, state the rate of change $\frac{dN}{dt}$.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 2 marks, testing your understanding of Derivatives of Basic Functions. It falls under Calculus 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 graphical treatment of limits, continuity and differentiability of functions of a single real variable, and differentiation, anti-differentiation and integration of these functions. This material is to be linked to applications in practical situations.
derivatives of $x^{\mathrm{n}}$ for $n \in Q, \varepsilon^{k}, \log _{e}(x), \sin (x), \cos (x)$ and $\tan (x)$
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State the derivative with respect to $x$ for each of the following functions: a. $f(x) = x^7$ b. $g(x) = e^{4x}$ c. $h(x) = \log_e(5x)$ d. $…
The population, $P$, of a newly discovered species of insect on a remote island is modelled by the equation $$P(t) = 1000 + 500 \cos(0.5t) +…
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