Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
3rd Edition
ISBN: 9780134763644
Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher: PEARSON
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Differential Equations
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Chapter 9, Problem 26RE

Logistic growth The population of a rabbit community is governed by the initial value problem

P ′ ( t ) = 0.2   P ( 1 − P 1200 ) , P ( 0 ) = 50.

  a.    Find the equilibrium solutions.

  b.    Find the population, for all times t ≥ 0.

  c.    What is the carrying capacity of the population?

  d.    What is the population when the growth rate is a maximum?

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Chapter 9 Solutions

Calculus: Early Transcendentals (3rd Edition)

Ch. 9.1 - What are the orders of the equations in Example 2?...Ch. 9.1 - What is the solution of the initial value problem...Ch. 9.1 - Solve the initial value problem in Example 4a with...Ch. 9.1 - Suppose the initial conditions in Example 5a are...Ch. 9.1 - In Example 7, if the height function were given by...Ch. 9.1 - Consider the differential equation y(t) + 9y(t) =...Ch. 9.1 - If the general solution of a differential equation...Ch. 9.1 - Does the function y(t) = 2t satisfy the...Ch. 9.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. 9.1 - The solution to the initial value problem y(t) = 2...
Ch. 9.1 - Explain why the graph of the solution to the...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying general solutions Verify that the given...Ch. 9.1 - Verifying solutions of initial value problems...Ch. 9.1 - Verifying solutions of initial value problems...Ch. 9.1 - Verifying solutions of initial value problems...Ch. 9.1 - Verifying solutions of initial value problems...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - Finding general solutions Find the general...Ch. 9.1 - General solutions Find the general solution of the...Ch. 9.1 - General solutions Find the general solution of the...Ch. 9.1 - General solutions Find the general solution of the...Ch. 9.1 - General solutions Find the general solution of the...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Solve the following...Ch. 9.1 - Solving initial value problems Find the solution...Ch. 9.1 - Solving initial value problems Find the solution...Ch. 9.1 - Solving initial value problems Find the solution...Ch. 9.1 - Solving initial value problems Find the solution...Ch. 9.1 - Motion in a gravitational field An object is fired...Ch. 9.1 - Prob. 44ECh. 9.1 - Harvesting problems Consider the harvesting...Ch. 9.1 - Harvesting problems Consider the harvesting...Ch. 9.1 - Draining tanks Consider the tank problem in...Ch. 9.1 - Prob. 48ECh. 9.1 - Explain why or why not Determine whether the...Ch. 9.1 - A second-order equation Consider the differential...Ch. 9.1 - Another second-order equation Consider the...Ch. 9.1 - Drug infusion The delivery of a drug (such as an...Ch. 9.1 - Logistic population growth Widely used models for...Ch. 9.1 - Free fall One possible model that describes the...Ch. 9.1 - Chemical rate equations The reaction of certain...Ch. 9.1 - Tumor growth The growth of cancer tumors may be...Ch. 9.2 - Assuming solutions are unique (at most one...Ch. 9.2 - Prob. 2QCCh. 9.2 - Prob. 3QCCh. 9.2 - Notice that the errors in Table 9.1 increase in...Ch. 9.2 - Explain how to sketch the direction field of the...Ch. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Identifying direction fields Which of the...Ch. 9.2 - Direction fields A differential equation and its...Ch. 9.2 - Prob. 8ECh. 9.2 - Direction fields with technology Plot a direction...Ch. 9.2 - Prob. 10ECh. 9.2 - Direction fields with technology Plot a direction...Ch. 9.2 - Sketching direction fields Use the window [2, 2] ...Ch. 9.2 - Sketching direction fields Use the window [2, 2] ...Ch. 9.2 - Sketching direction fields Use the window [2, 2] ...Ch. 9.2 - Sketching direction fields Use the window [2, 2] ...Ch. 9.2 - Sketching direction fields Use the window [2, 2] ...Ch. 9.2 - Increasing and decreasing solutions Consider the...Ch. 9.2 - Increasing and decreasing solutions Consider the...Ch. 9.2 - Increasing and decreasing solutions Consider the...Ch. 9.2 - Increasing and decreasing solutions Consider the...Ch. 9.2 - Logistic equations Consider the following logistic...Ch. 9.2 - Logistic equations Consider the following logistic...Ch. 9.2 - Logistic equations Consider the following logistic...Ch. 9.2 - Logistic equations Consider the following logistic...Ch. 9.2 - Two steps of Eulers method For the following...Ch. 9.2 - Two steps of Eulers method For the following...Ch. 9.2 - Two steps of Eulers method For the following...Ch. 9.2 - Two steps of Eulers method For the following...Ch. 9.2 - Errors in Eulers method Consider the following...Ch. 9.2 - Errors in Eulers method Consider the following...Ch. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Equilibrium solutions A differential equation of...Ch. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Equilibrium solutions A differential equation of...Ch. 9.2 - Equilibrium solutions A differential equation of...Ch. 9.2 - Direction field analysis Consider the first-order...Ch. 9.2 - Eulers method on more general grids Suppose the...Ch. 9.2 - Analyzing models The following models were...Ch. 9.2 - Prob. 47ECh. 9.2 - Analyzing models The following models were...Ch. 9.2 - Convergence of Eulers method Suppose Eulers method...Ch. 9.2 - Stability of Eulers method Consider the initial...Ch. 9.3 - Which of the following equations are separable?...Ch. 9.3 - Write y(t) = (t2 + 1)/y3 in separated form.Ch. 9.3 - Find the value of the constant C in Example 2 with...Ch. 9.3 - Find the value of the constant C in Example 3 with...Ch. 9.3 - What is a separable first-order differential...Ch. 9.3 - Is the equation t2y(t)=t+4y2 separable?Ch. 9.3 - Is the equation y(t)=2yt separable?Ch. 9.3 - Explain how to solve a separable differential...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving separable equations Find the general...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solutions of separable equations Solve the...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solving initial value problems Determine whether...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Solutions in implicit form Solve the following...Ch. 9.3 - Logistic equation for a population A community of...Ch. 9.3 - Logistic equation for an epidemic When an infected...Ch. 9.3 - Explain why or why not Determine whether the...Ch. 9.3 - Implicit solutions for separable equations For the...Ch. 9.3 - Implicit solutions for separable equations For the...Ch. 9.3 - Orthogonal trajectories Two curves are orthogonal...Ch. 9.3 - Orthogonal trajectories Use the method in Exercise...Ch. 9.3 - Applications 44.Logistic equation for spread of...Ch. 9.3 - Free fall An object in free fall may be modeled by...Ch. 9.3 - Free fall Using the background given in Exercise...Ch. 9.3 - Torricellis law An open cylindrical tank initially...Ch. 9.3 - Chemical rate equations Let y(t) be the...Ch. 9.3 - Tumor growth The Gompertz growth equation is often...Ch. 9.3 - Blowup in finite time Consider the initial value...Ch. 9.3 - Analysis of a separable equation Consider the...Ch. 9.4 - Verify by substitution that y(t) = Cekt b/k is a...Ch. 9.4 - Prob. 2QCCh. 9.4 - Prob. 3QCCh. 9.4 - Prob. 4QCCh. 9.4 - In general, what is the equilibrium temperature...Ch. 9.4 - The general solution of a first-order linear...Ch. 9.4 - Prob. 2ECh. 9.4 - What is the general solution of the equation y'(t)...Ch. 9.4 - Prob. 4ECh. 9.4 - First-order linear equations Find the general...Ch. 9.4 - First-order linear equations Find the general...Ch. 9.4 - First-order linear equations Find the general...Ch. 9.4 - First-order linear equations Find the general...Ch. 9.4 - First-order linear equations Find the general...Ch. 9.4 - First-order linear equations Find the general...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Initial value problems Solve the following initial...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Stability of equilibrium points Find the...Ch. 9.4 - Loan problems The following initial value problems...Ch. 9.4 - Loan problems The following initial value problems...Ch. 9.4 - Loan problems The following initial value problems...Ch. 9.4 - Loan problems The following initial value problems...Ch. 9.4 - Newtons Law of Cooling Solve the differential...Ch. 9.4 - Newton's Law of Cooling Solve the differential...Ch. 9.4 - Newtons Law of Cooling Solve the differential...Ch. 9.4 - Prob. 30ECh. 9.4 - Intravenous drug dosing The amount of drug in the...Ch. 9.4 - Optimal harvesting rate Let y(t) be the population...Ch. 9.4 - Endowment model An endowment is an investment...Ch. 9.4 - Explain why or why not Determine whether the...Ch. 9.4 - Prob. 36ECh. 9.4 - A bad loan Consider a loan repayment plan...Ch. 9.4 - Prob. 38ECh. 9.4 - Special equations A special class of first-order...Ch. 9.4 - Prob. 40ECh. 9.4 - Special equations A special class of first-order...Ch. 9.4 - Prob. 42ECh. 9.4 - Prob. 43ECh. 9.4 - Prob. 44ECh. 9.4 - General first-order linear equations Consider the...Ch. 9.4 - Prob. 46ECh. 9.4 - Prob. 47ECh. 9.4 - General first-order linear equations Consider the...Ch. 9.5 - Explain why the maximum growth rate for the...Ch. 9.5 - Prob. 2QCCh. 9.5 - Prob. 3QCCh. 9.5 - Explain how the growth rate function determines...Ch. 9.5 - Prob. 2ECh. 9.5 - Explain how the growth rate function can be...Ch. 9.5 - Prob. 4ECh. 9.5 - Is the differential equation that describes a...Ch. 9.5 - What are the assumptions underlying the...Ch. 9.5 - Describe the solution curves in a predator-prey...Ch. 9.5 - Prob. 8ECh. 9.5 - Solving logistic equations Write a logistic...Ch. 9.5 - Solving logistic equations Write a logistic...Ch. 9.5 - Designing logistic functions Use the method of...Ch. 9.5 - Designing logistic functions Use the method of...Ch. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Solving the Gompertz equation Solve the Gompertz...Ch. 9.5 - Prob. 22ECh. 9.5 - Stirred tank reactions For each of the following...Ch. 9.5 - Stirred tank reactions For each of the following...Ch. 9.5 - Stirred tank reactions For each of the following...Ch. 9.5 - Stirred tank reactions For each of the following...Ch. 9.5 - Prob. 31ECh. 9.5 - Growth rate functions a.Show that the logistic...Ch. 9.5 - Solution of the logistic equation Use separation...Ch. 9.5 - Properties of the Gompertz solution Verify that...Ch. 9.5 - Properties of stirred tank solutions a.Show that...Ch. 9.5 - Prob. 36ECh. 9.5 - RC circuit equation Suppose a battery with voltage...Ch. 9.5 - U.S. population projections According to the U.S....Ch. 9 - Explain why or why not Determine whether the...Ch. 9 - Prob. 2RECh. 9 - General solutions Use the method of your choice to...Ch. 9 - General solutions Use the method of your choice to...Ch. 9 - General solutions Use the method of your choice to...Ch. 9 - Prob. 6RECh. 9 - General solutions Use the method of your choice to...Ch. 9 - General solutions Use the method of your choice to...Ch. 9 - General solutions Use the method of your choice to...Ch. 9 - Prob. 10RECh. 9 - Solving initial value problems Use the method of...Ch. 9 - Prob. 12RECh. 9 - Solving initial value problems Use the method of...Ch. 9 - Prob. 14RECh. 9 - Solving initial value problems Use the method of...Ch. 9 - Solving initial value problems Use the method of...Ch. 9 - Solving initial value problems Use the method of...Ch. 9 - Solving initial value problems Use the method of...Ch. 9 - Direction fields Consider the direction field for...Ch. 9 - Direction fields The direction field for the...Ch. 9 - Eulers method Consider the initial value problem...Ch. 9 - Equilibrium solutions Find the equilibrium...Ch. 9 - Equilibrium solutions Find the equilibrium...Ch. 9 - Equilibrium solutions Find the equilibrium...Ch. 9 - Equilibrium solutions Find the equilibrium...Ch. 9 - Logistic growth The population of a rabbit...Ch. 9 - Logistic growth parameters A cell culture has a...Ch. 9 - Logistic growth in India The population of India...Ch. 9 - Stirred tank reaction A 100-L tank is filled with...Ch. 9 - Newtons Law of Cooling A cup of coffee is removed...Ch. 9 - A first-order equation Consider the equation...Ch. 9 - A second-order equation Consider the equation...

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