This is the question down there.

Question

After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1991?, 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 9?% of the radioactive isotope? remains, how long did the farmers need to wait to use this? hay?

Answer 1

You can set this up as an exponential decay problem.

 

Amount of isotope remaining:

 

N(t) = N(0)e^-kt

 

t_1/2 = 6 days

 

N(t + t_1/2) = (1/2) N(t)

 

N(0)e^-kte^-kt_1/2 = (1/2) N(0)e^-kt

 

e^-6k = 1/2

 

k = -ln(0.5) / 6 = 0.1155 days^-1

 

N(t) = N(0)e^-0.1155t

 

Let T = time when N = 9% = 0.09

 

0.09 = 1*e^-0.1155T

 

T = -ln(0.09) / 0.1155 = 20.848 days