nuclear decay answer key
}{N_0} = \left(\frac{1}{2}\right)^n \] where \( n \) is the number of half-lives. Solve for \( n \): \[ 0.125 = \left(\frac{1}{2}\right)^n \] \[ n = \log_{1/2}(0.125) = \log_{1/2}(2^{-3}) = 3 \] Calculate total time: \[ t = n \times t_{1/2} = 3 \times 3 = 9 \text{ hours}