The time-dependent growth of a bacterial population is governed by the equation
\[
\frac{dx}{dt}=x\left(1-\frac{x}{200}\right),
\]
where \(x\) is the population size at time \(t\). The initial population size is \(x_0=100\) at \(t=0\). As \(t\to\infty\), the population size of bacteria asymptotically approaches ________________________.