Question 327293: A certian population obeys the latural law of decay. at a certian time,the population is 40,000. three years later the population is 38000. approximately how long does it take the population to decline from 40,000 to 20,000?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A certain population obeys the natural law of decay. at a certian time,the population is 40,000. three years later the population is 38000. approximately how long does it take the population to decline from 40,000 to 20,000?
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You have two points (0,40000) and (3,38000)
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Assuming the decay is exponential, use the
model A(t) = ab^t
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Solve for a and b
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Using (0,40000), solve for "a":
40,000 = ab^0
a = 40,000
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Now, A(t) = 40,000*b^t
Using (3,38000), solve for "b":
38000, = 40,000*b^3
19/20 = b^3
b = 0.983
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Equation:
A(t) = 40000*0.983^t
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When does the population decay to 20,000?
20,000 = 40000*0.983^t
0.983^t = 0.5
t = log(0.5)/log(0.983)
t is approximately 40
Rounded up you would get 41 years
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Cheers,
Stan H.
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