A population of a particular yeast cell develops with a constant relative growth rate of 0.4311 per hour. The initial population consists of 3.9 million cells. Find the population size (in millions of cells) after 5 hours. (Round your answer to one decimal place.)

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18-07-2022
Mathematics

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A population of a particular yeast cell develops with a constant relative growth rate of 0.4311 per hour. The initial population consists of 3.9 million cells. Find the population size (in millions of cells) after 5 hours. (Round your answer to one decimal place.)

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aryanagarwal466 aryanagarwal466 · Answer 1 · 2022-07-21T14:55:58+02:00

A population of a particular yeast cell develops with a constant relative growth rate of [tex]0.4311[/tex] per hour. The initial population consists of [tex]3.9[/tex]million cells. Find the population size (in millions of cells) after 5 hours. Population size after [tex]5hrs[/tex] is [tex]33.6million[/tex].

How can we find the population size ?

The projection of population growth in yeast is given by

[tex]N=N_{0} e^{rt}[/tex]

Where [tex]N_{0}[/tex]=initial population which is [tex]3.9million[/tex]

[tex]r[/tex]=intrinsic rate of natural increases which is [tex]0.4311million per hour[/tex]

N is population size

Substitute the values

[tex]N=N_{0} e^{rt}\\N=3.9(e^{0.4311*5} )\\\\N=33.6 million[/tex]

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