Answer
(a) $C(t) = \frac{30t}{200+t}$
(b) The concentration as $t \to \infty$ approaches $30~g/L$
Work Step by Step
(a) We can write an expression for the amount of salt (in grams )after $t$ minutes:
$(30)(25)(t)$
We can write an expression for the amount of water (in liters) after $t$ minutes:
$5000+25t$
We can find the concentration after $t$ minutes:
$C(t) = \frac{(30)(25)(t)}{5000+25t} = \frac{30t}{200+t}$
(b) We can find the concentration as $t \to \infty$:
$\lim\limits_{t \to \infty}C(t) = \lim\limits_{t \to \infty}\frac{30t}{200+t} = \lim\limits_{t \to \infty}\frac{30t/t}{200/t+t/t} = \frac{30}{0+1} = 30$
The concentration as $t \to \infty$ approaches $30~g/L$
