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 46 days). If it is safe to feed the hay to cows when 10% 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 $LaTeX: \displaystyle k = \frac{\ln 2}{46}$ . This gives the equation $LaTeX: \displaystyle 0.1 = e^{-\frac{\ln(2)}{46}t}$ Taking the natural logarithm of both sides gives $LaTeX: \displaystyle \ln(0.1)= \frac{-t\ln(2)}{46}$ . Solving for $LaTeX: \displaystyle t$ gives $LaTeX: \displaystyle t = -\frac{ 46\ln(0.1) }{ \ln(2) }$ . The farmers had to wait about 152.8 days.