After the release of radioactive material into the atmospher

After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1998, the hay in that country was contaminated by a radioactive isotope (half-life 8 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? The farmers needed to wait approximately nothing days for it to be safe to feed the hay to the cows. (Round to one decimal place as needed.)

Solution

half life of radioactive material is 8 days

A = Ao e^ kt

1/2 Ao = Ao e^8k

calculating k from here

ln ( 1/2) = 8k

k = -.08664

finding time when 15% radioactive isotope remains

.15Ao = Ao e^ (-.08664 t )

ln ( .15) = -.08664 t

t = 21.89 = 22 days approximately