Question

A tank contains 9000 L of pure water. Brine that contains 40 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) = 40t 360 + t . As t → ∞, what does the concentration approach? g

Answer 1

Step-by-step explanation:

The concentration of salt after t minutes is given by :

`C(t)=(40t)/(360+t)`

A tank contains 9000 L of pure water. Brine that contains 40 g of salt per liter of water is pumped into the tank at a rate of 25 L/min.

We need to find the concentration approach at
`t\rightarrow \infty`

So,
`\lim_(t \to \infty)C(t)=(40t)/(360+t)`

`\lim_(t \to \infty)C(t)=(40)/((360)/(t)+1)`

Put
`t=\infty`

`\lim_(t \to \infty)C(t)=(40)/((360)/(\infty)+1)`

Since,
`(360)/(\infty)=0`

C(t) = 40 g/L

So, at
`t\rightarrow \infty` the concentration approaches to 40 g/L. Hence, this is the required solution.