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 45 weeks). If it is safe to feed the hay to cows when 27% 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 $LaTeX: \displaystyle k = \frac{\ln 2}{45}$ . This gives the equation $LaTeX: \displaystyle 0.27 = e^{-\frac{\ln(2)}{45}t}$ Taking the natural logarithm of both sides gives $LaTeX: \displaystyle \ln(0.27)= \frac{-t\ln(2)}{45}$ . Solving for $LaTeX: \displaystyle t$ gives $LaTeX: \displaystyle t = -\frac{ 45\ln(0.27) }{ \ln(2) }$ . The farmers had to wait about 85.00000000 weeks.