Chemical Mixture A 100-gallon tank is full of a solution containing 25 pounds of a concentrate. Starting at time t = 0 , distilled water is admitted to the tank at the rate of 10 gallons per minute, and the well-stirred solution is withdrawn at the same rate. (a) Find the amount Q of the concentrate in the solution as a function of t by solving the differential equation Q ' = − 10 ( Q 100 ) . (b) Find the time required for the amount of concentrate in the tank to reach 15 pounds.

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
BuyFind

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

Solutions

Chapter
Section
Chapter 11.4, Problem 27E
Textbook Problem

Chemical Mixture A 100-gallon tank is full of a solution containing 25 pounds of a concentrate. Starting at time t =   0 , distilled water is admitted to the tank at the rate of 10 gallons per minute, and the well-stirred solution is withdrawn at the same rate.

(a) Find the amount Q of the concentrate in the solution as a function of t by solving the differential equation

Q ' = 10 ( Q 100 ) .

(b) Find the time required for the amount of concentrate in the tank to reach 15 pounds.

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Chapter 11 Solutions

Calculus: An Applied Approach (MindTap Course List)
Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Verifying Solutions In Exercises 1-12, verify the...Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Finding a Particular Solution In Exercises 21-24,...Ch. 11.1 - Finding a Particular Solution In Exercises 21-24,...Ch. 11.1 - Finding a Particular Solution In Exercises 21-24,...Ch. 11.1 - Finding a Particular Solution In Exercises 21-24,...Ch. 11.1 - Finding a Particular Solution In Exercises 2528,...Ch. 11.1 - Finding a Particular Solution In Exercises 2528,...Ch. 11.1 - Finding a Particular Solution In Exercises 2528,...Ch. 11.1 - Finding a Particular Solution In Exercises 2528,...Ch. 11.1 - Sketching Graphs of Solutions In Exercises 29 and...Ch. 11.1 - Sketching Graphs of Solutions In Exercises 29 and...Ch. 11.1 - Finding the General Solution In Exercises 31-38,...Ch. 11.1 - Finding the General Solution In Exercises 31-38,...Ch. 11.1 - Finding the General Solution In Exercises 31-38,...Ch. 11.1 - Finding the General Solution In Exercises 31-38,...Ch. 11.1 - Finding the General Solution In Exercises 31-38,...Ch. 11.1 - Finding the General Solution In Exercises 31-38,...Ch. 11.1 - Finding the General Solution In Exercises 31-38,...Ch. 11.1 - Finding the General Solution In Exercises 31-38,...Ch. 11.1 - Biology The limiting capacity of the habitat of a...Ch. 11.1 - Investment The rate of growth of an investment is...Ch. 11.1 - Safety Assume the rate of change per hour in the...Ch. 11.1 - HOW DO YOU SEE IT? 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Weight Gain A...Ch. 11.2 - In Exercises 1-4, verify the solution of the...Ch. 11.2 - In Exercises 1-4, verify the solution of the...Ch. 11.2 - In Exercises 1-4, verify the solution of the...Ch. 11.2 - In Exercises 1-4, verify the solution of the...Ch. 11.2 - In Exercises 5 and 6, verify that the general...Ch. 11.2 - In Exercises 5 and 6, verify that the general...Ch. 11.2 - In Exercises 7-10, use separation of variables to...Ch. 11.2 - In Exercises 7-10, use separation of variables to...Ch. 11.2 - In Exercises 7-10, use separation of variables to...Ch. 11.2 - In Exercises 7-10, use separation of variables to...Ch. 11.2 - In Exercises 11 and 12, (a) find the general...Ch. 11.2 - In Exercises 11 and 12, (a) find the general...Ch. 11.2 - In Exercises 13 and 14, use the initial condition...Ch. 11.2 - In Exercises 13 and 14, use the initial condition...Ch. 11.2 - Find an equation of the graph that passes through...Ch. 11.2 - Ignoring resistance, a sailboat starting from rest...Ch. 11.3 - Checkpoint 1 Worked-out solution available at...Ch. 11.3 - Checkpoint 2 Worked-out solution available at...Ch. 11.3 - Checkpoint 3 Worked-out solution available at...Ch. 11.3 - In Exercises 1-4, simplify the expression....Ch. 11.3 - In Exercises 1-4, simplify the expression....Ch. 11.3 - In Exercises 1-4, simplify the expression. elnx3Ch. 11.3 - In Exercises 1-4, simplify the expression. e2lnx+xCh. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - Writing in Standard Form In Exercises 1-6, write...Ch. 11.3 - Writing in Standard Form In Exercises 1-6, write...Ch. 11.3 - Writing in Standard Form In Exercises 1-6, write...Ch. 11.3 - Writing in Standard Form In Exercises 1-6, write...Ch. 11.3 - Writing in Standard Form In Exercises 1-6, write...Ch. 11.3 - Writing in Standard Form In Exercises 1-6, write...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Using Two Methods In Exercises 19-22, solve for y...Ch. 11.3 - Using Two Methods In Exercises 19-22, solve for y...Ch. 11.3 - Using Two Methods In Exercises 19-22, solve for y...Ch. 11.3 - Using Two Methods In Exercises 19-22, solve for y...Ch. 11.3 - Matching In Exercises 23-26, match the...Ch. 11.3 - Matching In Exercises 23-26, match the...Ch. 11.3 - Matching In Exercises 23-26, match the...Ch. 11.3 - Matching In Exercises 23-26, match the...Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Sales The rate of change (in thousands of units)...Ch. 11.3 - HOW DO YOU SEE IT? 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Solving a Differential Equation In Exercises 43...Ch. 11 - Finding a Particular Solution In Exercises 45-48,...Ch. 11 - Finding a Particular Solution In Exercises 45-48,...Ch. 11 - Finding a Particular Solution In Exercises 4548,...Ch. 11 - Finding a Particular Solution In Exercises 45-48,...Ch. 11 - Finding an Equation In Exercises 49 and 50, find...Ch. 11 - Finding an Equation In Exercises 49 and 50, find...Ch. 11 - Radioactive Decay The rate of decomposition of...Ch. 11 - Advertising Awareness A newly opened chiropractors...Ch. 11 - Writing in Standard Form In Exercises 53-56, write...Ch. 11 - Writing in Standard Form In Exercises 53-56, write...Ch. 11 - Writing in Standard Form In Exercises 53-56, write...Ch. 11 - Writing in Standard Form In Exercises 53-56, write...Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Finding a Particular Solution In Exercises 65 and...Ch. 11 - Finding a Particular Solution In Exercises 65 and...Ch. 11 - Safety Assume the rate of change per hour in the...Ch. 11 - Chemistry A wet shirt hung from a clothesline to...Ch. 11 - Economics: Paretos Law According to the economist...Ch. 11 - Economics: Paretos Law In 2013, 29.7 million...Ch. 11 - Chemical Reaction During a chemical reaction, a...Ch. 11 - Chemical Reaction Using the result of Exercise 71,...Ch. 11 - Chemistry: Newtons Law of Cooling In Exercises 73...Ch. 11 - Chemistry: Newtons Law of Cooling In Exercises 73...Ch. 11 - Biology A population of 12 pelicans has been...Ch. 11 - Chemical Mixture A tank contains 30 gallons of a...Ch. 11 - Chemical Mixture A tank contains 20 gallons of a...Ch. 11 - In Exercises 1 and 2, verify the solution of the...Ch. 11 - 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