Question 456221: An endangered species of fish has a population that is decreasing exponentially Assume continuous decay. The population 8 years ago was 1600. Today, only 700 of the fish are alive. Once the population drops below 100, the situation will be irreversible. When will this happen, according to the model? (Round to the nearest whole year.)
A. 19 years from today
B. 20 years from today
C. 21 years from today
D. 18 years from today
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An endangered species of fish has a population that is decreasing exponentially Assume continuous decay. The population 8 years ago was 1600. Today, only 700 of the fish are alive. Once the population drops below 100, the situation will be irreversible. When will this happen, according to the model? (Round to the nearest whole year.)
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y = ab^x
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Let x = 0 represent "8 years ago".
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1600 = ab^0
a = 1600
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Today is represented by x = 8.
700 = 1600b^8
b^8 = 7/16
b = (7/16)^(1/8)
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Equation:
y = 1600*(7/16)^(x/8)
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Solve:
100 = 1600*(7/16)^(x/8)
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1/16 = (7/16)^(x/8)
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Take the log of both sides and solve for "x":
(x/8)*log(7/16) = log(1/16)
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x/8 = 3.3539
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x = 26.83 years
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Cheers,
Stan H.
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A. 19 years from today
B. 20 years from today
C. 21 years from today
D. 18 years from today
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