Pregunta
Growth of a bacteria population
(in millions), at time
(hours), follows the logisic
growth
(a) Sketch the graph of the bacteria population verses time, for the first eight hours.
(b) What is the initial population size?
(d) What value does the bacteria population approach after large time?
growth
(b) What is the initial population size?
(d) What value does the bacteria population approach after large time?
Ask by Horton Ortiz. in Qatar
Dec 13,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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(a) Sketch the graph of the bacteria population versus time for the first eight hours. The graph starts at 0.5 million and approaches 4 million.
(b) The initial population size is 0.5 million.
© The population approaches 4 million as time goes to infinity.
(b) The initial population size is 0.5 million.
© The population approaches 4 million as time goes to infinity.
Solución

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Como
Mind Expander
To visualize the growth of the bacteria population over time, let’s start by assessing the formula provided:
The function
shows a logistic growth pattern. When we sketch the graph for the first eight hours (where
ranges from 0 to 8), we see an initial slow growth which sharply increases and then levels off as it approaches the carrying capacity. Overall, the graph will be S-shaped (sigmoid curve).
For part (b), the initial population size is calculated by substituting
into the equation. This yields:
Thus, the initial population size is 0.5 million bacteria or 500,000 bacteria.
For part (d), to determine the value that the bacteria population approaches as time goes to infinity, we can consider the limit of
as
approaches infinity. As
becomes infinitesimally small, the value of
approaches:
Therefore, the bacteria population approaches 4 million after a long duration.

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