After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1982, 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 11% of the radioactive isotope remains, how long did the farmers need to wait to use this hay?

25.48 days

Step-by-step explanation:

For a radioactive substance, the Amount of the substance remaining A(t) is modeled by the equation

where

In the given problem:

Half Life of the Radioactive Isotope = 8

Initial Amount, =100%=1

A(t)=11% =0.11

Therefore substituting in the model above:

The farmer need to wait for 25.48 days

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get