Question

A tank contains 9000 L of pure water. Brine that contains 20 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 (in grams per liter) is C(t) = 20t/360+t As t → [infinity], what does the concentration approach?

Answer 1

Answer:

20 g/L

Explanation:

To know what happens with the concentration, we must calcute the limit of the function where t → ∞. The limit is the value that the function approach when t intend to a value. So:

$\lim_{t \to \infty} C(t) =  \lim_{t \to \infty}\frac{20t}{360 + t}$

Dividing both for "t"

$\lim_{t \to \infty} C(t) =  \lim_{t\to \infty} \frac{\frac{1}{t}20t }{\frac{1}{t}(360 + t) }$

$\lim_{t \to \infty} \frac{20}{\frac{360}{t} + 1 }$

The limit of 1/t when t intend to infity is 0, which is demonstrated in the graph below, so:

$\lim_{t\to \infty} 20 = 20$

The concentration will approach 20 g/L.