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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275361

Chapter 6.2, Problem 24E

Textbook Problem

Finding an Exponential Function In

Exercises 23-26, find the exponential function

Calculus of a Single Variable

Ch. 6.1 - Verifying a Solution Describe how to determine...Ch. 6.1 - General Solution What does the general solution of...Ch. 6.1 - Slope Field What do the line segments on a slope...Ch. 6.1 - Euler's Method What docs Eulers Method allow you...Ch. 6.1 - Verifying a Solution In Exercises 510, verify that...Ch. 6.1 - Verifying a Solution In Exercises 510, verify that...Ch. 6.1 - Verifying a Solution In Exercises 510, verify that...Ch. 6.1 - Verifying a Solution In Exercises 510, verify that...Ch. 6.1 - Verifying a Solution In Exercises 510, verify that...Ch. 6.1 - Verifying a Solution In Exercises 510, verify that...

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The graph shows a solution of...Ch. 6.1 - EXPLORING CONCEPTS Euler's Method Explain when...Ch. 6.1 - EXPLORING CONCEPTS Finding Values II is known that...Ch. 6.1 - True or False? In Exercises 87 and 88, determine...Ch. 6.1 - True or False? In Exercises 87 and 88, determine...Ch. 6.1 - Errors and Eulers Method The exact solution of the...Ch. 6.1 - Errors and Eulers Method Repeat Exercise 89 for...Ch. 6.1 - Electric Circuit The diagram shows a simple...Ch. 6.1 - Slope Field A slope field shows that the slope at...Ch. 6.1 - Think About It It is known that y=Asint is a...Ch. 6.1 - Think About It It is known that y=ekt is a...Ch. 6.1 - PUTNAM EXAM CHALLENGE Let f be a...Ch. 6.1 - Prove that if the family of integral curves of the...Ch. 6.2 - CONCEPT CHECK Describing Values Describe what the...Ch. 6.2 - CONCEPT CHECK Growth and Decay For y=Cekt, explain...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Writing and Solving a Differential Equation In...Ch. 6.2 - Writing and Solving a Differential Equation In...Ch. 6.2 - Slope Field In Exercises 15 and 16, a differential...Ch. 6.2 - Slope Field In Exercises 15 and 16, a differential...Ch. 6.2 - Finding a Particular Solution In Exercises 17-20,...Ch. 6.2 - Finding a Particular Solution In Exercises 17-20,...Ch. 6.2 - Finding a Particular Solution In Exercises 17-20,...Ch. 6.2 - Finding a Particular Solution In Exercises 17-20,...Ch. 6.2 - Writing and Solving a Differential Equation In...Ch. 6.2 - Writing and Solving a Differential Equation In...Ch. 6.2 - Finding an Exponential Function In Exercises...Ch. 6.2 - Finding an Exponential Function In Exercises...Ch. 6.2 - Finding an Exponential Function In Exercises...Ch. 6.2 - Finding an Exponential Function In Exercises...Ch. 6.2 - EXPLORING CONCEPTS Increasing Function In...Ch. 6.2 - EXPLORING CONCEPTS Increasing Function In...Ch. 6.2 - Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay Radioactive radium has a...Ch. 6.2 - Carbon Dating Carbon-14 dating assumes that the...Ch. 6.2 - Compound Interest In Exercises 39-44, complete the...Ch. 6.2 - Compound Interest In Exercises 39-44, complete the...Ch. 6.2 - Compound Interest In Exercises 39-44, complete the...Ch. 6.2 - Compound Interest In Exercises 39-44, complete the...Ch. 6.2 - Compound Interest In Exercises 39-44, complete the...Ch. 6.2 - Compound Interest In Exercises 39-44, complete the...Ch. 6.2 - Compound Interest In Exercises 45-48, Find the...Ch. 6.2 - Compound Interest In Exercises 45-48, find the...Ch. 6.2 - Compound Interest In Exercises 45-48, Find the...Ch. 6.2 - Compound Interest In Exercises 45-48, Find the...Ch. 6.2 - Compound Interest In Exercises 49 and 50, find the...Ch. 6.2 - Compound Interest In Exercises 49 and 50, find the...Ch. 6.2 - Population In Exercises 51-54, the population (in...Ch. 6.2 - Population In Exercises 51-54, the population (in...Ch. 6.2 - Population In Exercises 51-54, the population (in...Ch. 6.2 - Population In Exercises 51-54, the population (in...Ch. 6.2 - Modeling Data One hundred bacteria are started in...Ch. 6.2 - Bacteria Growth The number of bacteria in a...Ch. 6.2 - Learning Curve The management at a certain factory...Ch. 6.2 - Learning Curve Suppose the management in Exercise...Ch. 6.2 - Insect Population (a) Suppose an insect population...Ch. 6.2 - HOW DO YOU SEE IT? The functions f and g are both...Ch. 6.2 - Modeling Data The table shows the cost of tuition...Ch. 6.2 - Forestry The value of a tract of timber is...Ch. 6.2 - Sound Intensity The level of sound (in decibels)...Ch. 6.2 - Noise Level With the installation of noise...Ch. 6.2 - Newton's Law of Cooling When an object is removed...Ch. 6.2 - Newton's Law of Cooling A container of hot liquid...Ch. 6.2 - True or False? In Exercises 67 and 68, determine...Ch. 6.2 - True or False? In Exercises 67 and 68, determine...Ch. 6.3 - Separation of Variaoles Determine whether each...Ch. 6.3 - Mutually Orthogonal What does it mean for two...Ch. 6.3 - Logistic Differential Equation List a real-life...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a General Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Finding a Particular Solution Curve In Exercises...Ch. 6.3 - Finding a Particular Solution Curve In Exercises...Ch. 6.3 - Finding a Particular Solution Curve In Exercises...Ch. 6.3 - Finding a Particular Solution Curve In Exercises...Ch. 6.3 - Using Slope In Exercises 33 and 34, find all...Ch. 6.3 - Using Slope In Exercises 33 and 34, find all...Ch. 6.3 - Slope Field In Exercises 35-38, (a) write a...Ch. 6.3 - Slope Field In Exercises 35-38, (a) write a...Ch. 6.3 - Slope Field In Exercises 35-38, (a) write a...Ch. 6.3 - Slope Field In Exercises 35-38, (a) write a...Ch. 6.3 - Radioactive Decay The rate of decomposition of...Ch. 6.3 - Chemical Reaction In a chemical reaction a certain...Ch. 6.3 - Weight Gain A calf that weighs 60 pounds at birth...Ch. 6.3 - Weight Gain A goat that weighs 7 pounds at birth...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - Finding Orthogonal Trajectories In Exercises...Ch. 6.3 - EXPLORING CONCEPTS Separation of Variables Is an...Ch. 6.3 - Slope Field Describe the slope field for a...Ch. 6.3 - Point of Inflection For any logistic equation,...Ch. 6.3 - Sailing Ignoring resistance, a sailboat starting...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Determining if a Function Is Homogeneous In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - Solving a Homogeneous Differential Equation In...Ch. 6.3 - True or False? In Exercises 83-85, determine...Ch. 6.3 - True or False? In Exercises 83-85, determine...Ch. 6.3 - True or False? In Exercises 83-85, determine...Ch. 6.3 - PUTNAM EXAM CHALLENGE A not uncommon calculus...Ch. 6.3 - CONCEPT CHECK Carrying Capacity Describe carrying...Ch. 6.3 - Finding a Particular Solution Using Separation of...Ch. 6.3 - Matching In Exercises 49-52, match the logistic...Ch. 6.3 - Matching In Exercises 49-52, match the logistic...Ch. 6.3 - Matching In Exercises 49-52, match the logistic...Ch. 6.3 - Matching In Exercises 49-52, match the logistic...Ch. 6.3 - Using a Logistic Equation In Exercises 53 and 54,...Ch. 6.3 - Using a Logistic Equation In Exercises 53 and 54,...Ch. 6.3 - Using a Logistic Differential Equation In...Ch. 6.3 - Using a Logistic Differential Equation In...Ch. 6.3 - Solving a Logistic Differential Equation In...Ch. 6.3 - Solving a Logistic Differential Equation In...Ch. 6.3 - Solving a Logistic Differential Equation In...Ch. 6.3 - Solving a Logistic Differential Equation In...Ch. 6.3 - Endangered Species A conservation organization...Ch. 6.3 - Bacteria Growth At time t=0. a bacterial culture...Ch. 6.3 - Finding a Derivative Show that if y=11+bekt, then...Ch. 6.3 - HOW DO YOU SEE IT? The growth of a population is...Ch. 6.4 - CONCEPT CHECK First-Order What does the term...Ch. 6.4 - CONCEPT CHECK First-Order Linear Differential...Ch. 6.4 - Determining Whether a Differential Equation Is...Ch. 6.4 - Determining Whether a Differential Equation Is...Ch. 6.4 - Determining Whether a Differential Equation Is...Ch. 6.4 - Determining Whether a Differential Equation Is...Ch. 6.4 - Solving a First-Order Linear Differential Equation...Ch. 6.4 - Solving a First-Order Linear Differential...Ch. 6.4 - Solving a First-Order Linear Differential Equation...Ch. 6.4 - Solving a First-Order Linear Differential Equation...Ch. 6.4 - Solving a First-Order Linear Differential Equation...Ch. 6.4 - Solving a First-Order Linear Differential Equation...Ch. 6.4 - Solving a First-Order Linear Differential Equation...Ch. 6.4 - Solving a First-Order Linear Differential Equation...Ch. 6.4 - Slope Field In Exercises 15 and 16, (a) sketch an...Ch. 6.4 - Slope Field In Exercises 15 and 16, (a) sketch an...Ch. 6.4 - Finding a Particular Solution In Exercises 17-24,...Ch. 6.4 - Finding a Particular Solution In Exercises 17-24,...Ch. 6.4 - Finding a Particular Solution In Exercises 17-24,...Ch. 6.4 - Finding a Particular Solution In Exercises 17-24,...Ch. 6.4 - Finding a Particular Solution In Exercises 17-24,...Ch. 6.4 - Finding a Particular Solution In Exercises 17-24,...Ch. 6.4 - Finding a Particular Solution In Exercises 17-24,...Ch. 6.4 - Finding a Particular Solution In Exercises 17-24,...Ch. 6.4 - Population Growth When predicting population...Ch. 6.4 - Investment Growth A large corporation starts at...Ch. 6.4 - Investment Growth In Exercises 27 and 28, use the...Ch. 6.4 - Investment Growth In Exercises 27 and 28, use the...Ch. 6.4 - Learning Curve The management at a certain factory...Ch. 6.4 - Intravenous Feeding Glucose is added intravenously...Ch. 6.4 - Falling Object In Exercises 31 and 32, consider an...Ch. 6.4 - Falling Object In Exercises 31 and 32, consider an...Ch. 6.4 - Electric Circuits In Exercises 33 and 34, use the...Ch. 6.4 - Electric CircuitsIn Exercises 33 and 34, use the...Ch. 6.4 - MixtureIn Exercises 3538, consider a tank that at...Ch. 6.4 - MixtureIn Exercises 3538, consider a tank that at...Ch. 6.4 - Mixture In Exercises 35-38, consider a tank that...Ch. 6.4 - Mixture In Exercises 35-38, consider a tank that...Ch. 6.4 - Using an Integrating Factor The expression u(x) is...Ch. 6.4 - HOW DO YOU SEE IT? The graph shows the amount of...Ch. 6.4 - EXPLORING CONCEPTS Using Different Methods...Ch. 6.4 - Integrating Factor Explain why you can omit the...Ch. 6.4 - Matching In Exercises 43-46, match the...Ch. 6.4 - Matching In Exercises 43-46, match the...Ch. 6.4 - Matching In Exercises 43-46, match the...Ch. 6.4 - Matching In Exercises 43-46, match the...Ch. 6.4 - Slope Field In Exercises 47 and 48, (a) use a...Ch. 6.4 - Slope Field In Exercises 47 and 48, (a) use a...Ch. 6.4 - Solving a First-Order Differential Equation In...Ch. 6.4 - Solving s First-Order Differential Equation In...Ch. 6.4 - Solving s First-Order Differential Equation In...Ch. 6.4 - Solving a First-Order Differential Equation In...Ch. 6.4 - Solving a First-Order Differential Equation In...Ch. 6.4 - Solving a First-Order Differential Equation In...Ch. 6.4 - Solving a First-Order Differential Equation In...Ch. 6.4 - Solving a First-Order Differential Equation In...Ch. 6.4 - Solving a Bernoulli Differential Equation In...Ch. 6.4 - Solving a Bernoulli Differential Equation In...Ch. 6.4 - Solving a Bernoulli Differential Equation In...Ch. 6.4 - Solving a Bernoulli Differential Equation In...Ch. 6.4 - Solving a Bernoulli Differential Equation In...Ch. 6.4 - Solving a Bernoulli Differential Equation In...Ch. 6.4 - Solving a Bernoulli Differential Equation In...Ch. 6.4 - Solving a Bernoulli Differential Equation In...Ch. 6.4 - True or False? In Exercises 65 and 66, determine...Ch. 6.4 - True or False? In Exercises 65 and 66, determine...Ch. 6 - Determining a Solution Determine whether the...Ch. 6 - Determining a Solution Determine whether the...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Slope Field In Exercises 9 and 10, a differential...Ch. 6 - Slope Field In Exercises 9 and 10, a differential...Ch. 6 - Slope Field In Exercises 11 and 12, (a) sketch the...Ch. 6 - Slope Field In Exercises 11 and 12, (a) sketch the...Ch. 6 - Euler's Method In Exercises 13 and 14, use Eulers...Ch. 6 - Euler's Method In Exercises 13 and 14, use Eulers...Ch. 6 - Solving a Differential Equation In Exercises 1522,...Ch. 6 - Solving a Differential Equation In Exercises 1522,...Ch. 6 - Solving a Differential Equation In Exercises 1522,...Ch. 6 - Solving a Differential Equation In Exercises 1522,...Ch. 6 - Solving a Differential Equation In Exercises 1522,...Ch. 6 - Solving a Differential Equation In Exercises 1522,...Ch. 6 - Solving a Differential Equation In Exercises 1522,...Ch. 6 - Solving a Differential Equation In Exercises 1522,...Ch. 6 - Writing and Solving a Differential Equation In...Ch. 6 - Writing and Solving a Differential Equation In...Ch. 6 - Finding an Exponential Function In Exercises 2528,...Ch. 6 - Finding an Exponential Function In Exercises 2528,...Ch. 6 - Finding an Exponential Function In Exercises 2528,...Ch. 6 - Finding an Exponential Function In Exercises...Ch. 6 - Air Pressure Under ideal conditions, air pressure...Ch. 6 - Radioactive Decay Radioactive radium has a...Ch. 6 - Population A population grows exponentially at a...Ch. 6 - Compound Interest Find the balance in an account...Ch. 6 - Sales The sales S (in thousands of units) of a new...Ch. 6 - Sales The sales S (in thousands of units) of a new...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Finding a Particular Solution Curve In Exercises...Ch. 6 - Finding a Particular Solution Curve In Exercises...Ch. 6 - Finding Orthogonal Trajectories In Exercises 45...Ch. 6 - Finding Orthogonal Trajectories In Exercises 45...Ch. 6 - Using a Logistic Equation In Exercises 47 and 48,...Ch. 6 - Using a Logistic Equation In Exercises 47 and 48,...Ch. 6 - Solving a Logistic Differential Equation In...Ch. 6 - Solving a Logistic Differential Equation In...Ch. 6 - Wildlife Population The rate of change of the...Ch. 6 - Environment A conservation department releases...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Finding a Particular Solution In Exercises 59-62,...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Doomsday Equation The differential equation...Ch. 6 - Sales Let S represent sales of a new product (in...Ch. 6 - Gompertz Equation Another model that can be used...Ch. 6 - Error Using the Product Rule Although it is true...Ch. 6 - Torricelli's Law Torricellis Law states that water...Ch. 6 - Torricelli's Law The cylindrical water tank shown...Ch. 6 - Torricelli's Law A tank similar to the one in...Ch. 6 - Rewriting the Logistic Equation Show that the...Ch. 6 - Biomass Biomass is a measure of the amount of...Ch. 6 - Epidemic Carriers are individuals who can transmit...Ch. 6 - If the tracer is injected instantaneously at time...Ch. 6 - Use the solution of the differential equation in...Ch. 6 - In Exercises 11 and 12, it was assumed that there...

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