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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