Air containing $0\mathrm{.}06\%$ carbon dioxide is pumped into a room whose volume is $12,000f{t}^3.$ The air is pumped in at a rate of $3,000f\frac{t^3}{m}in,$ and the circulated air is then pumped out at the same rate. If there is an initial concentration of $0\mathrm{.}4\%$ carbon dioxide, determine the subsequent amount $A(t),$ in $f{t}^3,$ in the room at time $t.$

$A(t)=$

What is the percent concentration of carbon dioxide at $10$ minutes? $($Round your answer to three decimal places.$)$

$\%$

What is the steady$-$state, or equilibrium, percent concentration of carbon dioxide?

$\%$