Q$1/$ a$-$ Determine $y(t)$ for a generic first$-$order transfer function shown if a step of magnitude $M$ is applied to $x(t)$

$\frac{(\frac{?}{\text{b}\text{a}\text{r}}(Y))(s)}{(\stackrel{}{x})(s)}=\frac{K}{s+1}$

b$-$ A first$-$order transfer function relating to height of fluid in a tank to inlet flow rate of the tank has gain of $10\frac{m}{\frac{m^3}{s}}$ and a time constant of $50sec.$ The system operating at steady state where inlet flow rate is $0\mathrm{.}4\frac{m^3}{s}$ and the fluid height in the tank is $3m.$ The inlet flow increased instantaneously to $0\mathrm{.}41\frac{m^3}{s}.$

What is the hieght of fluid in tank $100sec$ after the increas has occurred?

What is the new steady state of fluid in the tank?