SOLUTION: After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1987, the hay in that country was contaminated by a radioactive isotope (ha

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Question 1147320: After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1987, the hay in that country was contaminated by a radioactive isotope (half life 6 days). If it is safe to feed the hay to the cows when 12% of the radioactive isotope remains, how long did the farmers need to wait to use this hay?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Solve .5%5Ex+=+.12 to find the number of half-lives it takes for the percentage to reach 12%; then multiply by the number of days in the half life to find the number of days.

The half life of 6 days is presumably an approximate number; and radioactive decay is random and not "smooth". So an approximation for an answer should be sufficient; using exactly 6 days for the half life and exactly 12% for the remaining percentage to get an answer to 5 or 6 decimal places is unrealistic.

Since .5^3 = .125 = 12.5%, the remaining percentage will be very close to 12% after 3 half lives, which is 3*6 = 18 days.