In a continous stirrer tank, $HCl$ solution decreased from $20\frac{\text{m}\text{o}\text{l}}{L}$ to $15\frac{\text{m}\text{o}\text{l}}{L}$ with using pure water.

Flow rates of inlet solution and pure water are $3\frac{L}{\text{m}\text{i}\text{n}}$ and $1\frac{L}{\text{m}\text{i}\text{n}}$ at steady state. V$=100L$ and doesn't change with time.

A$)$ Find the transfer function of $C_A$ and $C_{Ai}.$

B$)$ After $2$ step change, obtain $C_A^{\text{'}}(t),$ ultimate value of $C_A,$ and time required to reach $95\%$ of ultimate value.

C$)$ Sketch the responses, change in $C_A$ and $C_{Ai}?$