To determine the half life of a radioactive element, a student plots a graph of $\ell \mathrm{n}\left|\frac{\mathrm{dN}(\mathrm{t})}{\mathrm{dt}}\right|$ versus t . Here $\frac{\mathrm{dN}(\mathrm{t})}{\mathrm{dt}}$ is the rate of radioactive decay at time $t$. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is