College Algebra math

Question

After the release of the radioactive material into the atmosphere from a nuclear power plant in the country 1995, the hay in that country was contaminated by a radioactive isotope (half-life 6 days) if it is safe to feed the cows when 12% of the radioactive isotope remains, how long did the farmers need to wait to use this hay?

Answer 1

half life 6 days

50% left after 6 days

25% left after 12 days

12.5% left after 18 days

wait a little more than 18 days

1/2 = e^6r

ln.5 = 6r

r = (ln.5)/6

12/100 = 3/25 = e^(t(ln.5)/6)

ln(.12) = t(ln.5)/6

t = 6ln.12/ln.5= about 18.35 days until 12% left

= about 18 days 8.48 hours

= about 18 days 8 hours 28 minutes, 50.49 seconds