Consider the Lotka-Volterra predator-prey model defined by d x d t = − 0.1 x + 0.02 x y d y d t = 0.2 y − 0.025 x y , where the populations x ( t ) (predators) and y ( t ) (prey) are measured in thousands. Suppose x (0) = 6 and y (0) = 6. Use a numerical solver to graph x ( t ) and y ( t ). Use the graphs to approximate the time t > 0 when the two populations are first equal. Use the graphs to approximate the period of each population.

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A First Course in Differential Equ...

11th Edition
Dennis G. Zill
Publisher: Cengage Learning
ISBN: 9781305965720
BuyFind

A First Course in Differential Equ...

11th Edition
Dennis G. Zill
Publisher: Cengage Learning
ISBN: 9781305965720

Solutions

Chapter 3.3, Problem 11E
Textbook Problem

Consider the Lotka-Volterra predator-prey model defined by

d x d t = 0.1 x + 0.02 x y d y d t = 0.2 y 0.025 x y ,

where the populations x(t) (predators) and y(t) (prey) are measured in thousands. Suppose x(0) = 6 and y(0) = 6. Use a numerical solver to graph x(t) and y(t). Use the graphs to approximate the time t > 0 when the two populations are first equal. Use the graphs to approximate the period of each population.

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Chapter 3 Solutions

A First Course in Differential Equations with Modeling Applications (MindTap Course List)
Ch. 3.1 - Carbon Dating Archaeologists used pieces of burned...Ch. 3.1 - The Shroud of Turin, which shows the negative...Ch. 3.1 - Newtons Law of Cooling/Warming A thermometer is...Ch. 3.1 - A thermometer is taken from an inside room to the...Ch. 3.1 - A small metal bar, whose initial temperature was...Ch. 3.1 - Two large containers A and B of the same size are...Ch. 3.1 - A thermometer reading 70 F is placed in an oven...Ch. 3.1 - At t = 0 a sealed test tube containing a chemical...Ch. 3.1 - A dead body was found within a closed room of a...Ch. 3.1 - The rate at which a body cools also depends on its...Ch. 3.1 - A tank contains 200 liters of fluid in which 30...Ch. 3.1 - Solve Problem 21 assuming that pure water is...Ch. 3.1 - A large tank is filled to capacity with 500...Ch. 3.1 - In Problem 23, what is the concentration c(t) of...Ch. 3.1 - Solve Problem 23 under the assumption that the...Ch. 3.1 - Determine the amount of salt in the tank at time t...Ch. 3.1 - A large tank is partially filled with 100 gallons...Ch. 3.1 - In Example 5 the size of the tank containing the...Ch. 3.1 - A 30-volt electromotive force is applied to an...Ch. 3.1 - Solve equation (7) under the assumption that E(t)...Ch. 3.1 - A 100-volt electromotive force is applied to an...Ch. 3.1 - A 200-volt electromotive force is applied to an...Ch. 3.1 - An electromotive force E(t)={120,0t200,t20 is...Ch. 3.1 - An LR-series circuit has a variable inductor with...Ch. 3.1 - Air Resistance In (14) of Section 1.3 we saw that...Ch. 3.1 - How High?No Air Resistance Suppose a small...Ch. 3.1 - How High?Linear Air Resistance Repeat Problem 36,...Ch. 3.1 - Skydiving A skydiver weighs 125 pounds, and her...Ch. 3.1 - Rocket Motion Suppose a small single-stage rocket...Ch. 3.1 - Rocket MotionContinued In Problem 39 suppose of...Ch. 3.1 - Evaporating Raindrop As a raindrop falls, it...Ch. 3.1 - Fluctuating Population The differential equation...Ch. 3.1 - Population Model In one model of the changing...Ch. 3.1 - Constant-Harvest model A model that describes the...Ch. 3.1 - Drug Dissemination A mathematical model for the...Ch. 3.1 - Memorization When forgetfulness is taken into...Ch. 3.1 - Heart Pacemaker A heart pacemaker, shown in Figure...Ch. 3.1 - Sliding Box (a) A box of mass m slides down an...Ch. 3.1 - Sliding Box—Continued In Problem 48 let s(t) be...Ch. 3.1 - What Goes Up (a) It is well known that the model...Ch. 3.2 - The number N(t) of supermarkets throughout the...Ch. 3.2 - The number N(t) of people in a community who are...Ch. 3.2 - A model for the population P(t) in a suburb of a...Ch. 3.2 - Census data for the United States between 1790 and...Ch. 3.2 - (a) If a constant number h of fish are harvested...Ch. 3.2 - Investigate the harvesting model in Problem 5 both...Ch. 3.2 - Repeat Problem 6 in the case a = 5, b = 1, h = 7.Ch. 3.2 - (a) Suppose a = b = 1 in the Gompertz differential...Ch. 3.2 - Two chemicals A and B are combined to form a...Ch. 3.2 - Solve Problem 9 if 100 grams of chemical A is...Ch. 3.2 - Leaking cylindrical tank A tank in the form of a...Ch. 3.2 - Leaking cylindrical tank—continued When friction...Ch. 3.2 - Leaking Conical Tank A tank in the form of a...Ch. 3.2 - Inverted Conical Tank Suppose that the conical...Ch. 3.2 - Air Resistance A differential equation for the...Ch. 3.2 - How High?Nonlinear Air Resistance Consider the...Ch. 3.2 - That Sinking Feeling (a) Determine a differential...Ch. 3.2 - Solar Collector The differential equation...Ch. 3.2 - Tsunami (a) A simple model for the shape of a...Ch. 3.2 - Evaporation An outdoor decorative pond in the...Ch. 3.2 - Doomsday equation Consider the differential...Ch. 3.2 - Doomsday or extinction Suppose the population...Ch. 3.2 - Skydiving A skydiver is equipped with a stopwatch...Ch. 3.2 - Hitting bottom A helicopter hovers 500 feet above...Ch. 3.2 - Old Man River In Figure 3.2.8(a) suppose that the...Ch. 3.2 - (a) Solve the DE in Problem 28 subject to y(1) =...Ch. 3.2 - Old Man River Keeps Moving ... Suppose the man in...Ch. 3.2 - The current speed vr of a straight river such as...Ch. 3.2 - Raindrops Keep Falling ... When a bottle of liquid...Ch. 3.2 - Time Drips By The clepsydra, or water clock, was a...Ch. 3.2 - (a) Suppose that a glass tank has the shape of a...Ch. 3.2 - Suppose that r = f(h) defines the shape of a water...Ch. 3.3 - We have not discussed methods by which systems of...Ch. 3.3 - In Problem 1 suppose that time is measured in...Ch. 3.3 - Use the graphs in Problem 2 to approximate the...Ch. 3.3 - Construct a mathematical model for a radioactive...Ch. 3.3 - Potassium-40 Decay The chemical element potassium...Ch. 3.3 - Potassium-Argon Dating The knowledge of how K-40...Ch. 3.3 - Consider two tanks A and B, with liquid being...Ch. 3.3 - Use the information given in Figure 3.3.6 to...Ch. 3.3 - Two very large tanks A and B are each partially...Ch. 3.3 - Three large tanks contain brine, as shown in...Ch. 3.3 - Consider the Lotka-Volterra predator-prey model...Ch. 3.3 - Show that a system of differential equations that...Ch. 3.3 - Determine a system of first-order differential...Ch. 3.3 - Show that the linear system given in (18)...Ch. 3.3 - SIR Model A communicable disease is spread...Ch. 3.3 - (a) In Problem 17, explain why it is sufficient to...Ch. 3.3 - Concentration of a Nutrient Suppose compartments A...Ch. 3.3 - The system in Problem 19, like the system in (2),...Ch. 3.3 - Mixtures Solely on the basis of the physical...Ch. 3.3 - Newtons Law of Cooling/Warming As shown in Figure...Ch. 3 - Answer Problems 1 and 2 without referring back to...Ch. 3 - Answer Problems 1 and 2 without referring back to...Ch. 3 - In March 1976 the world population reached 4...Ch. 3 - Air containing 0.06% carbon dioxide is pumped into...Ch. 3 - tzi the Iceman In September of 1991 two German...Ch. 3 - In the treatment of cancer of the thyroid, the...Ch. 3 - Solve the differential equation dydx=ya2y2 of the...Ch. 3 - Suppose a cell is suspended in a solution...Ch. 3 - Suppose that as a body cools, the temperature of...Ch. 3 - According to Stefans law of radiation the absolute...Ch. 3 - Suppose an RC-series circuit has a variable...Ch. 3 - A classical problem in the calculus of variations...Ch. 3 - A model for the populations of two interacting...Ch. 3 - Initially, two large tanks A and B each hold 100...Ch. 3 - When all the curves in a family G(x, y, c1) = 0...Ch. 3 - When all the curves in a family G(x, y, c1) = 0...Ch. 3 - When all the curves in a family G(x, y, c1) = 0...Ch. 3 - When all the curves in a family G(x, y, c1) = 0...Ch. 3 - With the identifications a = r, b = r/K, and a/b =...Ch. 3 - Sawing Wood A long uniform piece of wood (cross...Ch. 3 - Solve the initial-value problem in Problem 20 when...Ch. 3 - Chemical Kinetics Suppose a gas consists of...

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