Math

CalculusCalculus: An Applied Approach (MindTap Course List)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t = 0 , distilled water is admitted to the tank at the rate of 10 gallons per minute, and the well-stirred solution is withdrawn at the same rate.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.BuyFind*launch*

10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

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

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

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

Calculus: An Applied Approach (MindTap Course List)

Ch. 11.1 - Checkpoint 1 Worked-out solution available at...Ch. 11.1 - Checkpoint2 Worked-out solution available at...Ch. 11.1 - Checkpoint 3 Worked-out solution available at...Ch. 11.1 - Checkpoint 4 Worked-out solution available at...Ch. 11.1 - In Exercises 1-4, find the first and second...Ch. 11.1 - In Exercises 1-4, find the first and second...Ch. 11.1 - In Exercises 1-4, find the first and second...Ch. 11.1 - In Exercises 1-4, find the first and second...Ch. 11.1 - In Exercises 5 and 6, solve for k. 0.5=99ekCh. 11.1 - In Exercises 5 and 6, solve for k. 14.75=2525e2k

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The graph shows a solution of...Ch. 11.1 - Verifying a Solution Show that y=a+Cek(1b)t is a...Ch. 11.1 - Using a Solution The function y=Cekx is a solution...Ch. 11.1 - True or False? In Exercises 45 and 46, determine...Ch. 11.1 - True or False? In Exercises 45 and 46, determine...Ch. 11.2 - Checkpoint 1 Worked-out solution available at...Ch. 11.2 - Checkpoint 2 Worked-out solution available at...Ch. 11.2 - Checkpoint 3 Worked-out solution available at...Ch. 11.2 - Checkpoint 4 Worked-out solution available at...Ch. 11.2 - Checkpoint 5 Worked-out solution available at...Ch. 11.2 - Checkpoint 6 Worked-out solution available at...Ch. 11.2 - In Exercises 1-6, find the indefinite integral....Ch. 11.2 - In Exercises 1-6, find the indefinite integral....Ch. 11.2 - In Exercises 1-6, find the indefinite integral....Ch. 11.2 - In Exercises 1-6, find the indefinite integral....Ch. 11.2 - In Exercises 1-6, find the indefinite integral....Ch. 11.2 - In Exercises 1-6, find the indefinite integral....Ch. 11.2 - In Exercises 7-10, solve the equation for C or k....Ch. 11.2 - In Exercises 7-10, solve the equation for C or k....Ch. 11.2 - In Exercises 7-10, solve the equation for C or k....Ch. 11.2 - In Exercises 7-10, solve the equation for C or k....Ch. 11.2 - Separation of Variables In Exercises 1-6, decide...Ch. 11.2 - Separation of Variables In Exercises 1-6, decide...Ch. 11.2 - Separation of Variables In Exercises 1-6, decide...Ch. 11.2 - Separation of Variables In Exercises 1-6, decide...Ch. 11.2 - Separation of Variables In Exercises 1-6, decide...Ch. 11.2 - Separation of Variables In Exercises 1-6, decide...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Solving a Differential equation In Exercises 2730,...Ch. 11.2 - Solving a Differential equation In Exercises 2730,...Ch. 11.2 - Solving a Differential equation In Exercises 2730,...Ch. 11.2 - Solving a Differential equation In Exercises 2730,...Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Finding an equation In Exercises 39 and 40, find...Ch. 11.2 - Finding an equation In Exercises 39 and 40, find...Ch. 11.2 - Velocity In Exercises 41 and 42, solve the...Ch. 11.2 - Velocity In Exercises 41 and 42, solve the...Ch. 11.2 - Biology: Cell Growth The growth rate of a...Ch. 11.2 - Solve the differential equation. HOW DO YOU SEE...Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Solve the differential equation. 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? The rate of change in the...Ch. 11.3 - Vertical Motion A falling object encounters air...Ch. 11.3 - Velocity A booster rocket carrying an observation...Ch. 11.3 - Learning Curve The management at a medical supply...Ch. 11.3 - Investment Let A he the amount in a fund earning...Ch. 11.4 - Checkpoint 1 Worked out solution available at...Ch. 11.4 - Checkpoint2 Worked-out solution available at...Ch. 11.4 - Checkpoint 3 Worked-out solution available at...Ch. 11.4 - Checkpoint 4 Worked-out solution available at...Ch. 11.4 - Checkpoint 5 Worked-out solution available at...Ch. 11.4 - In Exercises 1-4, use separation of variables to...Ch. 11.4 - In Exercises 1-4, use separation of variables to...Ch. 11.4 - In Exercises 1-4, use separation of variables to...Ch. 11.4 - In Exercises 1-4, use separation of variables to...Ch. 11.4 - In Exercises 5-8, use an integrating factor to...Ch. 11.4 - In Exercises 5-8, use an integrating factor to...Ch. 11.4 - In Exercises 5-8, use an integrating factor to...Ch. 11.4 - In Exercises 5-8, use an integrating factor to...Ch. 11.4 - In Exercises 9 and 10, solve for k. 300=150e4kCh. 11.4 - In Exercises 9 and 10, solve for k. 0.36=1e7kCh. 11.4 - Chemical Reaction In Exercises 1 and 2, use the...Ch. 11.4 - Chemical Reaction In Exercises 1 and 2, use the...Ch. 11.4 - Advertising Awareness In Exercises 3 and 4, use...Ch. 11.4 - Advertising Awareness In Exercises 3 and 4, use...Ch. 11.4 - Population Growth In Exercises 5 and 6, use the...Ch. 11.4 - Population Growth In Exercises 5 and 6, use the...Ch. 11.4 - Hybrid Selection In Exercises 7 and 8, use the...Ch. 11.4 - Hybrid Selection In Exercises 7 and 8, use the...Ch. 11.4 - Finding a Particular Solution In Exercises 9-14,...Ch. 11.4 - Finding a Particular Solution In Exercises 9-14,...Ch. 11.4 - Finding a Particular Solution In Exercises 9-14,...Ch. 11.4 - Finding a Particular Solution In Exercises 9-14,...Ch. 11.4 - Finding a Particular Solution In Exercises 9-14,...Ch. 11.4 - Finding a Particular Solution In Exercises 914,...Ch. 11.4 - Chemical Reaction During a chemical reaction, a...Ch. 11.4 - Chemical Reaction Using the result of Exercise 15,...Ch. 11.4 - Population Growth The rate of change of the...Ch. 11.4 - Chemistry A wet towel hung from a clothesline to...Ch. 11.4 - Sales Growth The rate of change in sales S (in...Ch. 11.4 - Sales Growth Use the result of Exercise 19 to find...Ch. 11.4 - Biology A population of eight beavers has been...Ch. 11.4 - Biology A population of 30 rabbits has been...Ch. 11.4 - Hybrid Selection You are studying a population of...Ch. 11.4 - Hybrid Selection A research team is studying a...Ch. 11.4 - Chemical Mixture A 100-gallon tank is full of a...Ch. 11.4 - Chemical Mixture A 200-gallon tank is half full of...Ch. 11.4 - Population Growth When predicting population...Ch. 11.4 - HOW DO YOU SEE IT? In a learning theory project,...Ch. 11.4 - Investment A large corporation starts at time t=0...Ch. 11.4 - Investment In Exercises 32-34, use the result of...Ch. 11.4 - Investment In Exercises 32-34, use the result of...Ch. 11.4 - Investment In Exercises 32-34, use the result of...Ch. 11.4 - Medical Science In Exercises 35-38, a medical...Ch. 11.4 - Medical Science In Exercises 35-38, a medical...Ch. 11.4 - Medical Science In Exercises 35-38, a medical...Ch. 11.4 - Medical Science In Exercises 35-38, a medical...Ch. 11 - Verifying Solutions In Exercises 1-10, verify the...Ch. 11 - Verifying Solutions In Exercises 1-10, verify the...Ch. 11 - Verifying Solutions In Exercises 1-10, verify the...Ch. 11 - Verifying Solutions In Exercises 1-10, verify the...Ch. 11 - Verifying Solutions In Exercises 1-10, verify the...Ch. 11 - Verifying Solutions In Exercises 1-10, verify the...Ch. 11 - Verifying Solutions In Exercises 1-10, verify the...Ch. 11 - Verifying Solutions In Exercises 1-10, verify the...Ch. 11 - Verifying Solutions In Exercises 1-10, verify the...Ch. 11 - Verifying Solutions In Exercises 1-10, verify the...Ch. 11 - Determining Solutions In Exercises 11-14,...Ch. 11 - Determining Solutions In Exercises 11-14,...Ch. 11 - Determining Solutions In Exercises 11-14,...Ch. 11 - Determining Solutions In Exercises 11-14,...Ch. 11 - Finding a Particular Solution In Exercises 15 and...Ch. 11 - Finding a Particular Solution In Exercises 15 and...Ch. 11 - Finding a Particular Solution In Exercises 17 and...Ch. 11 - Finding a Particular Solution In Exercises 17 and...Ch. 11 - Sketching Graphs of Solutions In Exercises 19 and...Ch. 11 - Sketching Graphs of Solutions In Exercises 19 and...Ch. 11 - Finding the General Solution In Exercises 21-26,...Ch. 11 - Finding the General Solution In Exercises 21-26,...Ch. 11 - Finding the General Solution In Exercises 21-26,...Ch. 11 - Finding the General Solution In Exercises 21-26,...Ch. 11 - Finding the General Solution In Exercises 21-26,...Ch. 11 - Finding the General Solution In Exercises 21-26,...Ch. 11 - Separation of Variables In Exercises 27-30, decide...Ch. 11 - Separation of Variables In Exercises 27-30, decide...Ch. 11 - Separation of Variables In Exercises 27-30, decide...Ch. 11 - Separation of Variables In Exercises 27-30, decide...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Solving a Differential Equation In Exercises 43...Ch. 11 - 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 - In Exercises 1 and 2, verify the solution of the...Ch. 11 - In Exercises 3-5, use separation of variables to...Ch. 11 - In Exercises 3-5, use separation of variables to...Ch. 11 - In Exercises 3-5, use separation of variables to...Ch. 11 - In Exercises 6-8, find the general solution of the...Ch. 11 - In Exercises 6-8, find the general solution of the...Ch. 11 - In Exercises 6-8, find the general solution of the...Ch. 11 - In Exercises 9-11, use the initial condition to...Ch. 11 - In Exercises 9-11, use the initial condition to...Ch. 11 - In Exercises 9-11, use the initial condition to...Ch. 11 - A lamb that weighs 10 pounds at birth gains weight...Ch. 11 - An infectious disease spreads through a large...

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