# "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?"

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
$P\left(t\right)=P\left(0\right){e}^{kt}=100$
b) Find the number of bacteria after 3 hours.
$P\left(t\right)=P\left(3\right){e}^{k3}=$ (confused as to how to set this up)
d) When will the population reach 10,000?
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Rayna Aguilar
$P\left(t\right)=100{e}^{kt}$
$P\left(1\right)=100{e}^{k\ast 1}=420$
$k=ln\left(4.2\right)$
b) is simply P(3)
c) solve P(x) = 10000

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