Draw a graph of time $t$ versus the number of undecayed nuclei in a radioactive sample and write its characteristics.

(N/A) The following characteristics are observed from the graph:
$(1)$ The number of undecayed nuclei in the radioactive sample decreases exponentially with time according to the law $N = N_0 e^{-\lambda t}$. In the beginning,the disintegration occurs quickly,and as time progresses,the rate of disintegration decreases. This graph is known as the decay curve.
$(2)$ From the graph,one can determine the rate of disintegration and the half-life $(T_{1/2})$.
$(3)$ If the decay constant $(\lambda)$ is large,the rate of disintegration is also large.
$(4)$ Regardless of the type of radioactive substance,it takes an infinite amount of time for the entire sample to decay completely.