Pearson eText University Calculus: Early Transcendentals -- Instant Access (Pearson+)
4th Edition
ISBN: 9780136880912
Author: Joel Hass, Christopher Heil
Publisher: PEARSON+
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Chapter 16, Problem 3GYR
To determine
The slope field of a differential equation y′=f(x,y).
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The spread of an infectious disease is often modeled using the following autonomous differential equation:
dI
-
- BI(N − I) − MI,
dt
where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of
transmission, and μ is the rate at which people recover from infection.
Close
a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria.
b) (5 points) For the equilbria in part a), determine whether each is stable or unstable.
c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the
dt
function by hand.) Identify the equilibria as stable or unstable in the graph.
d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.
Find the indefinite integral.
Check
Answer:
7x
4 + 1x
dx
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Chapter 16 Solutions
Pearson eText University Calculus: Early Transcendentals -- Instant Access (Pearson+)
Ch. 16.1 - In Exercises 1–4, match the differential equations...Ch. 16.1 - In Exercises 1–4, match the differential equations...Ch. 16.1 - In Exercises 1–4, match the differential equations...Ch. 16.1 - In Exercises 1–4, match the differential equations...Ch. 16.1 - In Exercises 5 and 6, copy the slope fields, and...Ch. 16.1 - In Exercises 5 and 6, copy the slope fields, and...Ch. 16.1 - Prob. 7ECh. 16.1 - Prob. 8ECh. 16.1 - Prob. 9ECh. 16.1 - Prob. 10E
Ch. 16.1 - Prob. 11ECh. 16.1 - Prob. 12ECh. 16.1 - Prob. 13ECh. 16.1 - Prob. 14ECh. 16.1 - In Exercises 15–20, use Euler’s method to...Ch. 16.1 - In Exercises 15–20, use Euler’s method to...Ch. 16.1 - Prob. 17ECh. 16.1 - Prob. 18ECh. 16.1 - Prob. 19ECh. 16.1 - Prob. 20ECh. 16.1 - Prob. 21ECh. 16.1 - Prob. 22ECh. 16.1 - Prob. 23ECh. 16.1 - Prob. 24ECh. 16.1 - Prob. 25ECh. 16.1 - Prob. 26ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 4ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 6ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 8ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 10ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 12ECh. 16.2 - Solve the differential equations in Exercises...Ch. 16.2 - Prob. 14ECh. 16.2 - Solve the initial value problems in Exercises...Ch. 16.2 - Prob. 16ECh. 16.2 - Solve the initial value problems in Exercises...Ch. 16.2 - Prob. 18ECh. 16.2 - Solve the initial value problems in Exercises...Ch. 16.2 - Prob. 20ECh. 16.2 - Solve the exponential growth/decay initial value...Ch. 16.2 - Solve the following initial value problem for u as...Ch. 16.2 - Prob. 23ECh. 16.2 - Prob. 24ECh. 16.2 - Prob. 25ECh. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Solve the Bernoulli equations in Exercises...Ch. 16.2 - Solve the Bernoulli equations in Exercises...Ch. 16.2 - Solve the Bernoulli equations in Exercises...Ch. 16.2 - Solve the Bernoulli equations in Exercises...Ch. 16.3 - Coasting bicycle A 66-kg cyclist on a 7-kg bicycle...Ch. 16.3 - Coasting battleship Suppose that an Iowa class...Ch. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.3 - Prob. 10ECh. 16.3 - Prob. 11ECh. 16.3 - Find the family of solutions of the given...Ch. 16.3 - Salt mixture A tank initially contains 100 gal of...Ch. 16.3 - Mixture problem A 200-gal is half full of...Ch. 16.3 - Fertilizer mixture A tank contains 100 gal of...Ch. 16.3 - Carbon monoxide pollution An executive conference...Ch. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.4 - Prob. 7ECh. 16.4 - Prob. 8ECh. 16.4 - Prob. 9ECh. 16.4 - Prob. 10ECh. 16.4 - Prob. 11ECh. 16.4 - Prob. 12ECh. 16.4 - Prob. 13ECh. 16.4 - Prob. 14ECh. 16.4 - Prob. 15ECh. 16.4 - Prob. 16ECh. 16.4 - Prob. 17ECh. 16.4 - The spread of information Sociologists recognize a...Ch. 16.4 - Prob. 19ECh. 16.4 - Prob. 20ECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16.5 - Prob. 3ECh. 16.5 - Prob. 4ECh. 16.5 - Consider another competitive-hunter model defined...Ch. 16.5 - Prob. 6ECh. 16.5 - Two trajectories approach equilibrium Show that...Ch. 16.5 - Prob. 8ECh. 16.5 - Prob. 9ECh. 16.5 - Prob. 10ECh. 16.5 - Prob. 11ECh. 16.5 - Prob. 12ECh. 16.5 - Prob. 13ECh. 16.5 - Prob. 14ECh. 16 - Prob. 1GYRCh. 16 - What is a general solution? What is a particular...Ch. 16 - Prob. 3GYRCh. 16 - Prob. 4GYRCh. 16 - Prob. 5GYRCh. 16 - Prob. 6GYRCh. 16 - Prob. 7GYRCh. 16 - Prob. 8GYRCh. 16 - Prob. 9GYRCh. 16 - Prob. 10GYRCh. 16 - Prob. 1PECh. 16 - Prob. 2PECh. 16 - Prob. 3PECh. 16 - Prob. 4PECh. 16 - Prob. 5PECh. 16 - Prob. 6PECh. 16 - Prob. 7PECh. 16 - Prob. 8PECh. 16 - Prob. 9PECh. 16 - Prob. 10PECh. 16 - Prob. 11PECh. 16 - Prob. 12PECh. 16 - Prob. 13PECh. 16 - Prob. 14PECh. 16 - Prob. 15PECh. 16 - Prob. 16PECh. 16 - Prob. 17PECh. 16 - Prob. 18PECh. 16 - Prob. 19PECh. 16 - Prob. 20PECh. 16 - Prob. 21PECh. 16 - Prob. 22PECh. 16 - Prob. 23PECh. 16 - Prob. 24PECh. 16 - Prob. 25PECh. 16 - Prob. 26PECh. 16 - Prob. 27PECh. 16 - Prob. 28PECh. 16 - Prob. 29PECh. 16 - Prob. 30PECh. 16 - Prob. 31PECh. 16 - Prob. 32PECh. 16 - Prob. 35PECh. 16 - Prob. 36PECh. 16 - Prob. 37PECh. 16 - Prob. 38PECh. 16 - Prob. 39PECh. 16 - Prob. 40PECh. 16 - Prob. 41PECh. 16 - Prob. 42PECh. 16 - Prob. 43PECh. 16 - Prob. 44PECh. 16 - Prob. 1AAECh. 16 - Prob. 2AAECh. 16 - Prob. 3AAECh. 16 - Prob. 4AAECh. 16 - Solve the homogeneous equations in Exercises 5–10....Ch. 16 - Prob. 6AAECh. 16 - Prob. 7AAECh. 16 - Prob. 8AAECh. 16 - Prob. 9AAECh. 16 - Prob. 10AAE
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