Answer
$${\text{3500}}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}p\left( t \right) = \frac{{3500t}}{{t + 1}} \cr
& {\text{Calculate }}\mathop {\lim }\limits_{t \to \infty } p\left( t \right) \cr
& {\text{ }}\mathop {\lim }\limits_{t \to \infty } p\left( t \right) = \mathop {\lim }\limits_{t \to \infty } \frac{{3500t}}{{t + 1}} \cr
& {\text{Divide th numerator and denominator by t}} \cr
& {\text{ }}\mathop {\lim }\limits_{t \to \infty } p\left( t \right) = \mathop {\lim }\limits_{t \to \infty } \frac{{\frac{{3500t}}{t}}}{{\frac{t}{t} + \frac{1}{t}}} \cr
& {\text{ }}\mathop {\lim }\limits_{t \to \infty } p\left( t \right) = \mathop {\lim }\limits_{t \to \infty } \frac{{3500}}{{1 + \frac{1}{t}}} \cr
& {\text{Evaluate }} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{\mathop {\lim }\limits_{t \to \infty } \left( {3500} \right)}}{{\mathop {\lim }\limits_{t \to \infty } \left( 1 \right) + \underbrace {\mathop {\lim }\limits_{t \to \infty } \left( {\frac{1}{t}} \right)}_{{\text{approaches to 0}}}}} = \frac{{3500}}{{1 + 0}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 3500 \cr
& {\text{Therefore}}{\text{, }} \cr
& {\text{The steady state exits}} \cr
& {\text{The steady - state value is 3500}} \cr} $$
