In 1986 a nuclear plant in Chernobyl former Soviet Union had

In 1986 a nuclear plant in Chernobyl (former Soviet Union) had a breakdown and spilled radioactive elements into the environment. In particular, it sent the radioisotope Iodine-131, denoted I131, over a large area of Eastern Europe. Suppose that in your hometown of Western Poland the levels of this isotope increased to 12 times the levels considered safe for living organisms. To avoid big doses of radiation, you leave your home and move to, say, South America. If the half-life of I131 is 8 days, when will the radioactivity levels drop enough for you to return safely home?

Solution

12 times the levels considered safe for living organisms ---- 12x

Now the levels to be dropped to x to be safe for return home safely -- x

half life = 8 dsy

decay constant = 0.693/8 = 0.086625 per day

N(t) = Noe^(-kt)

x = 12xe^(-0.086625t)

(1/12) =e^(-0.086625t)

ln(1/12) = -0.086625t

t = 28.68 days