The half-life of a radioactive decay is ${}^{\prime }x{}^{\prime }$ times its mean life. The value of $x$ is

To determine the half life of a radioactive element, student plots a graph of $ln|dN(t)/dt|$ versus $t$. Here $dN(t)/dt$ 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 ......