The product C N 1 and interpret its meaning given that the matrix C represents the cost per text message and cost per minute over the maximum number of minutes allowed and matrix N 1 represents the number of text messages and the number of minutes over the maximum incurred for 1 month and matrix N 3 represents the number of minutes over the maximum for 3 months.
The product C N 1 and interpret its meaning given that the matrix C represents the cost per text message and cost per minute over the maximum number of minutes allowed and matrix N 1 represents the number of text messages and the number of minutes over the maximum incurred for 1 month and matrix N 3 represents the number of minutes over the maximum for 3 months.
Solution Summary: The author calculates the product CN_1 and interprets its meaning.
To calculate: The product CN1 and interpret its meaning given that the matrix C represents the cost per text message and cost per minute over the maximum number of minutes allowed and matrix N1 represents the number of text messages and the number of minutes over the maximum incurred for 1 month and matrix N3 represents the number of minutes over the maximum for 3 months.
(b)
To determine
To calculate: The product CN3 and interpret its meaning given that the matrix C represents the cost per text message and cost per minute over the maximum number of minutes allowed and matrix N1 represents the number of text messages and the number of minutes over the maximum incurred for 1 month and matrix N3 represents the number of minutes over the maximum for 3 months.
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.
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