i do not know how to solve this problem?

Question

After the release of radio active material into the atmosphere from a nuclear power plant in a country in 1989, the hay in that country was contaminated by a radioactive isotope (half-life 7 days). If it is safe to feed the hay to cows when 15% of the radioactive isotope remains, how long did the farmers need to wait to use this hay?

Answer 1

0.15a₀ = a₀(0.5^t/7

0.15 = 0.5^t/7

ln 0.15 = (t/7)(ln 0.50

-1.897 ≈ (t/7)(¡-0.693)

2.732 ≈ t/7

19.127 ≈ t