Question 98507: An herbicide loses one-half its toxic effect each week. After how many weeks will the herbicide have less than 10 percent of its original potency?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An herbicide loses one-half its toxic effect each week. After how many weeks
will the herbicide have less than 10 percent of its original potency?
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let Po be the original potency.
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If you figure the answer in days
Po(1/2)^(t/7) < 0.10Po
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Divide both sides by Po to get:
(1/2)^(t/7) < 0.10
Take the log to get:
(t/2)log(1/2)
Since log(1/2) is negative you get:
(t/7) > [log0.10]/[log(1/2)
t/7 > 3.32
t > 23.25 days
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Starting with the 24th day, the percentage will be < 10% of the original amount.
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Cheers,
Stan H.
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