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

The concentration of salt approaches 20 grams per liter.

Step-by-step explanation:

The concentration of salt after t minutes is given by the equation C(t) = 20t/360+t. To find the concentration as t approaches infinity, we can take the limit of C(t) as t approaches infinity. Let's evaluate the limit:

lim[t->∞] (20t)/(360+t)

Using L'Hôpital's rule, we can differentiate the numerator and denominator:

lim[t->∞] 20/(1+0)

Therefore, the concentration approaches 20 grams per liter.

Answer 2

20 g/L

Step-by-step 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)(20t)/(360 + t)`

Dividing both for "t"

`\lim_(t \to \infty) C(t) =  \lim_(t\to \infty) ((1)/(t)20t )/((1)/(t)(360 + t) )`

`\lim_(t \to \infty) (20)/((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.