SOLUTION: After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1981 ​, the hay in that country was contaminated by a radioactive

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1981 ​, the hay in that country was contaminated by a radioactive       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1128536: After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1981
​,
the hay in that country was contaminated by a radioactive isotope​ (half-life 7

​days). If it is safe to feed the hay to cows when 15
​%
of the radioactive isotope​ remains, how long did the farmers need to wait to use this​ hay?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1981​, the hay in that country was contaminated by a radioactive isotope​ (half-life 7 ​days).
If it is safe to feed the hay to cows when 15​% of the radioactive isotope​ remains, how long did the farmers need to wait to use this​ hay?
:
Using the radio-active decay formula; A+=+Ao%2A2%5E%28-t%2Fh%29, where
A = resulting amt after t time
Ao = initial amt
t = time in days
h = half-life in days
:
let A=1, the Ao= .15
:
1%2A2%5E%28%28-t%2F7%29%29+=+.15
-t%2F7 = ln%28.15%29%2Fln%282%29
-t%2F7 = -2.737
t = -7 * -2.737
t = +19.158 days, say cow can start eating it in 20 days safely