Physicists using the radioactivity equation y = y₀e^-kt call the number 1/k the mean life of a radioactive nucleus. The mean life of a radon nucleus is about 1/0.18 = 5.6 days. The mean life of a carbon-14 nucleus is more than 8000 years. Show that 95% of the radioactive nuclei originally present in a sample will disintegrate within three mean lifetimes, i.e., by time t = 3/k. Thus, the mean life of a nucleus gives a quick way to estimate how long the radioactivity of a sample will last.