MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS
8th Edition
ISBN: 9780357537343
Author: Johnson
Publisher: CENGAGE L
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Chapter A, Problem 14E
To determine
To calculate:
The value of
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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 A Solutions
MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS
Ch. A - Prob. 1ECh. A - Prob. 2ECh. A - Prob. 3ECh. A - Prob. 4ECh. A - Prob. 5ECh. A - Prob. 6ECh. A - Prob. 7ECh. A - Prob. 8ECh. A - Prob. 9ECh. A - Prob. 10E
Ch. A - Prob. 11ECh. A - Prob. 12ECh. A - Prob. 13ECh. A - Prob. 14ECh. A - Prob. 15ECh. A - Prob. 16ECh. A - Prob. 17ECh. A - Prob. 18ECh. A - Prob. 19ECh. A - Prob. 20ECh. A - Prob. 21ECh. A - Prob. 22ECh. A - Prob. 23ECh. A - Prob. 24ECh. A - Perform the calculations in Exercises 1-32. The...Ch. A - Perform the calculations in Exercises 1-32. The...Ch. A - Prob. 27ECh. A - Prob. 28ECh. A - Perform the calculations in Exercises 1-32. The...Ch. A - Prob. 30ECh. A - Prob. 31ECh. A - Perform the calculations in Exercises 1-32. The...Ch. A - Solve 4.2x2+8.3x+1.1=0 for x. Check your two...Ch. A - Solve 5.7x2+12.3x8.1=0 for x. Check your two...Ch. A - Prob. 35E
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