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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

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

c ( t ) = 30 t 200 + t

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

(a)

To determine

To show: The concentration of salt after t minutes is C(t)=30t200+t.

Explanation

Proof:

The volume of the tank is 5000L initially.

The volume of the tank increases by 25L per minute

Therefore, the volume of the tank at time t is 5000+25t .

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 30×25=750 grams per minute.

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

Concentration of the salt after time t=Amount of saltVolume o

(b)

To determine

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

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