Math question radioactive material

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

5

​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?

The farmers needed to wait approximately

enter your response here

days for it to be safe to feed the hay to the cows?

Answer 1

If they wait 1 day, there will be 50% of the isotope remaining

If they wait 2 days, there will be 25% of the isotope remaining

If they wait 3 days, there will be 12.5% of the isotope remaining

If they wait 4 days, there will be 6.25% of the isotope remaining

So after 4 days it will be safe.

If you need a more precise answer you need to find the answer to the equation

0.5^x = 0.11

You may either use logarithms or solve it graphically depending on what methods you were taught.

The answer is x = 3.1844 days or

3 days 4 hours 25 minutes and 32 seconds