Answer:

Since we have no information about X(t), we choose $x = X/(K \, y_{XS})$.

$$\begin{eqnarray*}\frac{d} {dt} S & = & - \dot{r}_m K f x\\ \frac{d} {dt} x & = & x f \dot{r}_m \end{eqnarray*}$$

with four parameters: S(0), x(0), K, $\dot{r}_m = j_S \, y_{XS}$. The latter parameter has the interpretation of the maximum specific growth rate.