After the release of radioactive material into the atmosphere from a nuclear power plant the hay in that country was contaminated by a radioactive isotope (half-life 86 weeks). If it is safe to feed the hay to cows when 28% of the radioactive isotope remains, how long did the farmers need to wait to use this hay? Round to the nearest tenth.

The decay constant is $LaTeX: \displaystyle k = \frac{\ln 2}{86}$ . This gives the equation $LaTeX: \displaystyle 0.28 = e^{-\frac{\ln(2)}{86}t}$ Taking the natural logarithm of both sides gives $LaTeX: \displaystyle \ln(0.28)= \frac{-t\ln(2)}{86}$ . Solving for $LaTeX: \displaystyle t$ gives $LaTeX: \displaystyle t = -\frac{ 86\ln(0.28) }{ \ln(2) }$ . The farmers had to wait about 157.9 weeks.