Question 698553: A bacteria culture has an initial population of 600. After 4 hours the population has grown to 1200. Assuming the culture grows at a rate proportional to the size of the population , find the function representing the population size after t hours and determine the size of the population after 8 hours.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A bacteria culture has an initial population of 600. After 4 hours the population has grown to 1200. Assuming the culture grows at a rate proportional to the size of the population , find the function representing the population size after t hours and determine the size of the population after 8 hours.
A(t) = Ao*b^t
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Using t = 4, Ao = 600 ; A(4) = 1200, solve for "b":
1200 = 600*b^4
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b^4 = 2
b = 2^(1/4) = 1.1892
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Equation:
A(t) = 600*(1.1892)^t
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A(8) = 600*(1.1892)^8
A(8) = 2400
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Cheers,
Stan H.
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