Question 1088727
After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1988​, the hay in that country was contaminated by a radioactive isotope​ (half-life 6 ​days).
 If it is safe to feed the hay to cows when 14​% of the radioactive isotope​ remains, how long did the farmers need to wait to use this​ hay?
:
using the radioactive decay formula: A = Ao*2^(-t/h), where
A = remaining amt after t time
Ao = initial amt
t = time of decay
h = half-life of substance
:
let initial amt = 1
then
resulting amt = .14 
:
1*2^(-t/6) = .14
use nat logs
ln(2^(-t/6)) = ln(.14)
the log equiv of exponents
{{{-t/6}}}*ln(2) = ln(.14
{{{-t/6}}} = {{{ln(.14)/ln(2)}}}
using your calc we have
{{{-t/6}}} = -2.8365
multiply both sides by -6
t = 17.02 days before using the hay