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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Mixture In Exercises 35-38, consider a tank that at time t = 0 contains v 0 gallons of a solution of which, by weight, q 0 pounds is soluble concentrate. Another solution containing q 1 pounds of the concentrate per gallon is running into the tank at the rate of r 1 gallons per minute. The solution in the tank is kept well stirred and is withdrawn at the rate of r 2 gallons per minute.

A 200-gallon tank is full of a solution containing 25 pounds of concentrate. Starting at time t = 0 , distilled water is

admitted to the tank at a rate of 10 gallons per minute, and the well-stirred solution is withdrawn at the same rate.

(a) Find the amount of concentrate Q (in pounds) in the solution as a function of t.

(b) Find die time at which the amount of concentrate in the lank reaches 15 pounds.

(c) Find die amount of concentrate (in pounds) in die solution as t .

a)

To determine

To Calculate: The amount Q of concentrate in the solution as a function of t.

Explanation

Given:

A 200-gallon tank is full of solution contains 25 pounds of concentrate starting at time t=0, distilled water is admitted to the tank at the rate of 10 gallons per minute and well stirred solution is withdrawn at the same rate.

Formula Used:

dQdt+r2Qv0+(r1r2)t=q1r1

Calculation:

Consider

dQdt+r2Qv0+(r1r2)t=q1r1

v0=200gallons

at t=0q0=25pounds

r1=10gallons/minute

q1=0(Distilled water)

r2=10gallons/minute

Substituting these values in equat

b)

To determine

To Calculate: The time when amount of concentrate in tank reaches 15 pounds.

c)

To determine

To Calculate: Theamount of concentrate (in pounds)in the solution as t.

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