SOLUTION: The number of bacteria in a culture begins with approximately 10,000 organisms at the start of an experiment. if the bacteria doubles every 5 hours find the following: a. A model

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Question 1102964: The number of bacteria in a culture begins with approximately 10,000 organisms at the start of an experiment. if the bacteria doubles every 5 hours find the following:
a. A model of the form P(t) = Poekt that represents the population P(t) of bacteria after t hours. Round k to 4 decimal places.
b. Determine the amount of time required for the population to grow to 2,000,000. Round to the nearest hour.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
p=10000e%5E%28kt%29
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20000=10000e%5E%285k%29
e%5E%285k%29=2
ln%28e%5E%285k%29%29=ln%282%29
5k=ln%282%29
k=ln%282%29%2F5

k=0.13862
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highlight%28p=10000e%5E%280.13862t%29%29
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Find t if p=2000000.
10000e%5E%280.13862t%29=2000000
e%5E%280.13862t%29=2000000%2F10000
e%5E%280.13862t%29=200
0.13862t=ln%28200%29
t=ln%28200%29%2F0.13862
highlight%28t=38.2%29
to the nearest hour, highlight%28highlight%28t=38%29%29