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A) a culture of bacteria is put in a Petri dish in doubles every 4 hours if the initial amount of bacteria is 100 how many bacteria will be in 15 hours( round to the nearest whole number)

B) When will the bacteria count be 350,000


Sagot :

At 15 hours the amount of bacteria is 1345. It takes 47 hours to get 350000 bacteria.

Let y represent the amount of bacteria after n hours

Since the bacteria doubles after every 4 hours, hence, this can be represented by exponential function:

y = abⁿ

where a is the initial value and b is the multiplier.

Since it doubles every 4 hours and the initial amount of bacteria is 100, this can be represented by:

a)

[tex]y=100(2)^\frac{n}{4}\\\\At\ 15hours:\\\\y=100(2)^\frac{15}{4}\\\\y=1345\ bacteria[/tex]

b) y = 350000

[tex]350000=100(2)^\frac{n}{4}\\\\3500=(2)^\frac{n}{4}\\\\taking\ ln:\\\\ln(3500)=\frac{n}{4} ln(2)\\\\\frac{n}{4}=11.77\\\\n=47\ hours[/tex]

Therefore at 15 hours the amount of bacteria is 1345. It takes 47 hours to get 350000 bacteria.

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