# The amount present in a radio active element disintegrates at a rate proportional to its amount .The differential equation corresponding to the above statement is ($k$ is negative)

$\begin{array}{1 1}(1)\frac{dp}{dt}=\frac{k}{p}&(2)\frac{dp}{dt}=kt\\(3)\frac{dp}{dt}=kp&(4)\frac{dp}{dt}=-kt\end{array}$

Let p be the amount present in a radio active element. Then
$\large\frac{dp}{dt} =kp$
Hence 3 is the correct answer.