CALCULUS+ITS APPLICATIONS
15th Edition
ISBN: 9780137590612
Author: Goldstein
Publisher: RENT PEARS
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Question
Chapter 12.2, Problem 9E
To determine
To calculate: The value of k, such that the function
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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 12 Solutions
CALCULUS+ITS APPLICATIONS
Ch. 12.1 - Compute the expected value and the variance of the...Ch. 12.1 - Prob. 2CYUCh. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Probability Table, Expected Value The number of...Ch. 12.1 - Prob. 7ECh. 12.1 - Prob. 8E
Ch. 12.1 - Decision Making Based on Expected Value A citrus...Ch. 12.1 - Prob. 10ECh. 12.2 - Prob. 1CYUCh. 12.2 - Prob. 2CYUCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - An experiment consists of selecting a point at...Ch. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - A random variable X has a cumulative distribution...Ch. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.3 - Prob. 1CYUCh. 12.3 - Prob. 2CYUCh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - Prob. 12ECh. 12.3 - Expected Reading Time The amount oftime (in...Ch. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - If X is a random variable with density function...Ch. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.4 - The emergency flasher on an automobile is...Ch. 12.4 - Prob. 2CYUCh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - In a large factory there is an average of two...Ch. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - During a certain part of the day, the time between...Ch. 12.4 - During a certain part of the day, the time between...Ch. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - Reliability of Electronic Components Suppose that...Ch. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Find the expected values and the standard...Ch. 12.4 - Prob. 17ECh. 12.4 - Find the expected values and the standard...Ch. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Normal Distribution and Life of a Tire Suppose...Ch. 12.4 - Amount of Milk in a Container If the amount of...Ch. 12.4 - Breaking weight Theamount of weight required to...Ch. 12.4 - Time of a commute A student with an eight oclock...Ch. 12.4 - Prob. 30ECh. 12.4 - Diameter of a Bolt A certain type of bolt must fit...Ch. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.5 - A public health officer is tracking down the...Ch. 12.5 - Suppose that a random variable X has a Poisson...Ch. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Number of Insurance Claims The monthly number of...Ch. 12.5 - Waiting Time in an Emergency Room On a typical...Ch. 12.5 - Prob. 7ECh. 12.5 - Number of Cars at a Tollgate During a certain part...Ch. 12.5 - Poisson Distribution in a Mixing Problem A bakery...Ch. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Quality Control The quality-control department at...Ch. 12.5 - Two Competing Companies In a certain town, there...Ch. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Prob. 23ECh. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - The number of accidents occurring each month at a...Ch. 12 - What is probability table?Ch. 12 - Prob. 2FCCECh. 12 - Prob. 3FCCECh. 12 - Prob. 4FCCECh. 12 - Prob. 5FCCECh. 12 - Prob. 6FCCECh. 12 - Prob. 7FCCECh. 12 - Prob. 8FCCECh. 12 - Prob. 9FCCECh. 12 - Give two ways to compute the variance of a...Ch. 12 - Prob. 11FCCECh. 12 - Prob. 12FCCECh. 12 - Prob. 13FCCECh. 12 - Prob. 14FCCECh. 12 - How is an integral involving a normal density...Ch. 12 - Prob. 16FCCECh. 12 - Prob. 17FCCECh. 12 - Let X be a continuous random variable on 0x2, with...Ch. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Probability of Gasoline Sales A certain gas...Ch. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Deciding on a Service Contract The condenser motor...Ch. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RECh. 12 - Area under the Normal Curve It is useful in some...Ch. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Rolling Dice A pair of dice is rolled until a 7 or...Ch. 12 - Rolling Dice A pair of dice is rolled until a 7 or...Ch. 12 - Rolling Dice A pair of dice is rolled until a 7 or...
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