A bacteria culture initially contains 100 cells and grows at

William Curry 2021-12-15 Answered
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420. Find the rate of growth after 3 hours.
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Expert Answer

Marcus Herman
Answered 2021-12-16 Author has 41 answers

From part(a), we know that
P(t)=100(4.2)t
Differentiate
P(t)=d[100(4.2)t] dt 
Recall that:
d(ax) dx =axlna
P(t)=100(4.2)tln4.2
P(t)=P(t)ln4.2
Substitute t=3
P(3)=P(3)ln4.2
From part (b), we know that P(3)=7409
P(3)=7409ln4.210633 Bacteria/hour
Result: P(3)=7409ln4.2106333 Bacteria/hour

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