If the sample of bacteria is growing at an hourly rate of 15% continuously and the bacteria began with 11 bacteria then there will be 244.178 samples bacteria after 21 hours.
Given growth of bacteria 15% ,bacteria at beginning 11.
We have to find the number of sample of bacteria after 21 hours.
We have to first form exponential function which shows the growth of bacteria in variable t.
Exponential function which shows the sum is y=P[tex]e^{rt}[/tex]
where P is initial amount ,
r is rate and
y is the sum
So in our problem P=11 and r=0.15
y=11*[tex]e^{0.15t}[/tex]
To find the samples after 21 hours we have to put t=21.
y=11[tex]e^{0.15*21}[/tex]
y=11*[tex]e^{3.1}[/tex]
y=11*22.198 ([tex]e^{3.1}[/tex]=22.198 from e table)
y=244.178
Hence the samples after 21 hours will be 244 approximately.
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