To determine the half life of a radioactive element, a student plots a graph of $$\ln \mid \frac{dN(t)}{dt} \mid$$ versus t. Here $$\frac{dN(t)}{dt}$$ 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