Chapter 2.6, Problem 68E

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8th Edition

James Stewart

ISBN: 9781305270336

Textbook Problem

(a) 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. Show that the concentration of salt after *t* minutes (in grams per liter) is

(b) What happens to the concentration as *t → ∞*?

(a)

To determine

**To show:** The concentration of salt after *t* minutes is

Explanation

**Proof:**

The volume of the tank is 5000L initially.

The volume of the tank increases by 25*L* per minute

Therefore, the volume of the tank at time *t* is

Concentration of brine in water which is entering tank is 30g per Litre.

The water is entering the tank at a rate of 25L per minute.

The amount of salt entering the tank is

Therefore, the amount of salt in the tank after *t* minutes is 750*t*.

(b)

To determine

**To find:** The value of concentration of the salt after *t* minutes when *t* approaches infinity.

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