PLEASE PROVIDE FULL WORKING OUT WITH SOLUTION Attached is the question The bacte

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PLEASE PROVIDE FULL WORKING OUT WITH SOLUTION

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The bacterium Escherichia coli. a common bacterium found in the human intestine grows at a rate proportional to the number of cells present. Under ideal laboratory conditions, the number of cells in a culture doubles every 20 minutes. The model we are using for this bacterium growth is Q(t) = Q0 times ekt Where Q is the number of cells present at time t (in minutes), the initial cell population (at t = 0) and k is the growth constant. If the initial cell population is 100, find the value of k that satisfies this model. How many cells will be present after 3.5 hours? You must use your model to answer this question. How long will it take for the initial colony of 100 cells to increase to a population of one million?

Explanation / Answer

half life period is 20 min
a)Q(t) = 100*( ekt )
t=20 min
Q(t)=2*Qo =200

==> 200=100*ekt

==> k=0.0347min-1

b) time=3.5 hrs

=210 min==>

Q(t) = 100*( ekt )

=100*(e0.0347*210)

=144815.47

c)

Q(t) =106 =100*(e0.0347*t)

t=265.43 min

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