Answer
$${\text{200}}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}m\left( t \right) = 200\left( {1 - {2^{ - t}}} \right) \cr
& {\text{Calculate }}\mathop {\lim }\limits_{t \to \infty } m\left( t \right) \cr
& {\text{ }}\mathop {\lim }\limits_{t \to \infty } m\left( t \right) = \mathop {\lim }\limits_{t \to \infty } 200\left( {1 - {2^{ - t}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 200\mathop {\lim }\limits_{t \to \infty } \left( {1 - {2^{ - t}}} \right) \cr
& {\text{Evaluate the limit}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 200\left[ {\mathop {\lim }\limits_{t \to \infty } \left( 1 \right) - \overbrace {\mathop {\lim }\limits_{t \to \infty } {2^{ - t}}}^{{\text{approaches to 0}}}} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 200\left( {1 - 0} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 200 \cr
& {\text{Therefore}}{\text{, }} \cr
& {\text{The steady state exits}} \cr
& {\text{The steady - state value is 200}} \cr} $$