The activity ($A$) of a radioactive sample is the number of disintegrations (decays) occurring per unit time. Mathematically, it is the magnitude of the rate of change of the number of nuclei: $A=|dN/dt|$. Since $dN/dt=-\lambda N$, the activity is also expressed as $A=\lambda N$, where $\lambda$ is the decay constant and $N$ is the number of radioactive nuclei present.