I need the answer to the question

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asked Dec 1, 2023 49.3k views

2 Answers

ConnectionLost · Answer 1 · 2023-12-05T10:10:14+0000

Answer: Following function gives the number of bacteria in a culture:

$n(t)=990e^(0.3t)\rightarrow(1)$

(a) The continues rate of growth can be found by taking the first time derivative of the equation (1), which is:

$\begin{gathered} R=(dn(t))/(dt)=(0.3*990)e^(0.3t) \\ R(t)=297e^(0.3t) \end{gathered}$

(b) The initial population can be found by plugging t = 0 in equation (1).

$\begin{gathered} n(0)=990e^((0.3*0))=990 \\ n(0)=990 \end{gathered}$

THerefore the answer is 9

(c) At t = 5, the number of bacteria in the culture would be:

$\begin{gathered} n(5)=990e^((0.3*5)) \\ n(5)=990e^((0.3*5)) \\ n(5)=4,436.8721 \end{gathered}$

Or roughly 4437 bacteria.