Q.Write two units of radioactivity. How are they interrelated?

Because $N = N_0 e^{-\lambda t}$ is exponential, taking $\log_{10}$ of both sides converts it into a straight line: $\log_{10}N = -\frac{\lambda}{2.303}t + \log_{10}N_0$. Since activity is directly proportional to N, the same straight-line relationship holds for $\log_{10}(\text{activity})$ plotted against time, with slope $-\frac{\lambda}{2.303}$ -- letting the decay constant be read directly off a real measured dataset without needing to know N0. Plotting raw activity (not its log) against time instead gives the familiar falling exponential curve. Radioactive dec …