Question

a tank contains 5000 l of pure water. brine that contains 30 g of salt per liter of water is pumped into the tank at a rate of 25 l/min. the concentration of salt after t minutes can be shown to be (c(t)=\frac{30t}{200 + t}). what happens to the concentration as (t
ightarrowinfty)? (lim_{t
ightarrowinfty}c(t)=square) g/l

Explanation:

Step1: Analyze the limit of the function

We need to find $\lim_{t
ightarrow\infty}C(t)$ where $C(t)=\frac{30t}{200 + t}$.

Step2: Divide numerator and denominator by $t$

$\lim_{t
ightarrow\infty}\frac{30t}{200 + t}=\lim_{t
ightarrow\infty}\frac{30}{\frac{200}{t}+1}$.

Step3: Evaluate the limit

As $t
ightarrow\infty$, $\frac{200}{t}
ightarrow0$. So $\lim_{t
ightarrow\infty}\frac{30}{\frac{200}{t}+1}=\frac{30}{0 + 1}=30$.

Answer:

30