$($a$)$ A tank contains $7000$ L of pure water. Brine that contains $20$ g of salt per liter of water is pumped into the tank at a rat of $25\frac{L}{m}in.$ Show that the concentration of salt $t$ minutes later $($in grams per liter$)$ is

$C(t)=\frac{20t}{280+t}$

After $t$ minutes $25t$ liters of brine with $20$ g of salt per liter has been pumped into the tank, so it contains

$$ liters of water and $$ grams of salt. Therefore, the salt concentration at time $t$ will be the following.

$C(t)=\frac{500t}{7000+25t}=\frac{20t}{280+t}\frac{g}{L}$

$($b$)$ What happens to the concentration as $t?$

$\underset{t}{lim}C(t)=,\frac{g}{L}$