Answer
$${\text{500}}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}p\left( t \right) = \frac{{1500}}{{3 + 2{e^{ - 0.1t}}}} \cr
& {\text{Calculate }}\mathop {\lim }\limits_{t \to \infty } p\left( t \right) \cr
& {\text{ }}\mathop {\lim }\limits_{t \to \infty } m\left( t \right) = \mathop {\lim }\limits_{t \to \infty } \frac{{1500}}{{3 + 2{e^{ - 0.1t}}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{1500}}{{3 + 2\left( 0 \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{1500}}{3} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 500 \cr
& {\text{Therefore, }} \cr
& {\text{The steady state exits}} \cr
& {\text{The steady - state value is 500}} \cr} $$
