F: A control system for heating a historical, $100-$year$-$old room is being designed.

The room can be modeled using the following equations

$T_{\text{r}\text{o}\text{o}\text{m}}=K_1{\displaystyle \underset{0}{\overset{t}{}}}{Q}_{0}d$

$Q_0=Q_{in}-Q_{\text{o}\text{u}\text{t}}$

$Q_{\text{o}\text{u}\text{t}}=K_2{T}_{\text{r}\text{o}\text{o}\text{m}}$

$Q_{in}=K_3(T_{\text{r}\text{a}\text{d}}-T_{\text{r}\text{o}\text{o}\text{m}})$

Where $T_{\text{r}\text{o}\text{o}\text{m}}$ is the room temperature and

$T_{\text{r}\text{a}\text{d}}$ is the radiator temperature. If the radiator temperature is $50$ degrees and if $K_1={10}^{-4},K_2=4,$ and $K_3=1,$ the change in the steady$-$state room temperature is most nearly

$10$

$30$

$40$

$50$

$20$