"A Bacteria Culture Contains 100 Cells and Grows at a Rate Proportional to its Size A bacteria culture contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420. a) Find and expression for the number of bacteria after t hours P(t)=P(0)e^kt=100 b) Find the number of bacteria after 3 hours. P(t)=P(3)e^k3= (confused as to how to set this up) d) When will the population reach 10,000?"

beobachtereb 2022-09-18 Answered
A Bacteria Culture Contains 100 Cells and Grows at a Rate Proportional to its Size
A bacteria culture contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420.
a) Find and expression for the number of bacteria after t hours
P ( t ) = P ( 0 ) e k t = 100
b) Find the number of bacteria after 3 hours.
P ( t ) = P ( 3 ) e k 3 = (confused as to how to set this up)
d) When will the population reach 10,000?
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Answers (1)

Rayna Aguilar
Answered 2022-09-19 Author has 14 answers
P ( t ) = 100 e k t
P ( 1 ) = 100 e k 1 = 420
k = l n ( 4.2 )
b) is simply P(3)
c) solve P(x) = 10000

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