Draw a graph showing the variation of decay rate with the number of active nuclei.

(N/A) According to the law of radioactive decay,the decay rate $R$ (or activity) is given by:
$R = \lambda N$
where $\lambda$ is the decay constant and $N$ is the number of active nuclei.
If we consider the rate of change of the number of nuclei,it is given by:
$\frac{dN}{dt} = -\lambda N$
Comparing this with the equation of a straight line $y = mx + c$,where $y = \frac{dN}{dt}$,$m = -\lambda$,$x = N$,and $c = 0$:
The graph of decay rate $(\frac{dN}{dt})$ versus the number of active nuclei $(N)$ is a straight line passing through the origin with a negative slope of $-\lambda$.
Since $N$ is always positive and $\frac{dN}{dt}$ is negative,the graph lies in the $4^{\text{th}}$ quadrant.