Question

After releasing of radioactive material into.The atnosphere from.A nuclear.Powe plant in a country in 1988, the hay in that country was contaminayed by radioactive.Isotope remains, how long did the famers need to.Wait to use this hay

Answer 1

Answer:

the question is incomplete, so I looked for a similar one:

After the release of radioactive material into the atmosphere  from a nuclear power plant, the hay was contaminated by iodine  131 ( half-life, 8 days). If it is all right to feed the hay to cows  when 10% of the iodine 131 remains, how long did the farmers  need to wait to use this hay?

iodine's half life (we are given x, we need to find b):

0.5A₀ = A₀eᵇˣ

x = 8 days

we eliminate A₀ from both sides

0.5 = eᵇ⁸

ln 0.5 = ln eᵇ⁸

-0.69315 = b8

b = -0.69315 / 8 = -0.08664

since the farmers need to wait until only 10% of the iodine remains (we already calculated b, now we need to find x):

0.1A₀ = A₀eᵇˣ

0.1 = eᵇˣ

ln 0.1 = bx

where b = -0.08664

x = ln 0.1 / -0.08664  = -2.302585 / -0.08664  = 26.58 days