An epidemic spreads through a population at a rate proportional to the product of the number of people already infected and the number of people susceptible, but not yet infected. Therefore, if S denotes the total population of susceptible people and I I(t) denotes the number of infected people at time t, then = I'= rI(S-I), where r is a positive constant. A) Let's say that there are 2000 susceptible people in a nursing home, so S = 2000. Let's also say that one infected person visits the home, so that I(0) = 1. Find the function I(t) for the number of peope infected at time t > 0. I(t) = B) If the infection rate is r = 0.0004, how many people are infected after t = 5 days? (Whole people only, please) C) As the value of t increases, can you see what I(t) become? In other words, calculate the following limit lim I(t) = t→∞
An epidemic spreads through a population at a rate proportional to the product of the number of people already infected and the number of people susceptible, but not yet infected. Therefore, if S denotes the total population of susceptible people and I I(t) denotes the number of infected people at time t, then = I'= rI(S-I), where r is a positive constant. A) Let's say that there are 2000 susceptible people in a nursing home, so S = 2000. Let's also say that one infected person visits the home, so that I(0) = 1. Find the function I(t) for the number of peope infected at time t > 0. I(t) = B) If the infection rate is r = 0.0004, how many people are infected after t = 5 days? (Whole people only, please) C) As the value of t increases, can you see what I(t) become? In other words, calculate the following limit lim I(t) = t→∞
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![An epidemic spreads through a population at a rate proportional to the product of the number of people
already infected and the number of people susceptible, but not yet infected. Therefore, if S denotes the
total population of susceptible people and I = I(t) denotes the number of infected people at time t, then
I'= rI(S – I),
where r is a positive constant.
A) Let's say that there are 2000 susceptible people in a nursing home, so S = 2000. Let's also say that one
infected person visits the home, so that I(0) = 1.
Find the function I(t) for the number of peope infected at time t > 0.
I(t) =
=
B) If the infection rate is r = 0.0004, how many people are infected after t
please)
5 days? (Whole people only,
C) As the value of t increases, can you see what I(t) become? In other words, calculate the following limit
lim I(t) =
=
t→∞](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb48e445-6f22-4655-aae5-a52568300bfa%2F6ce2ffd8-661c-4262-8bb0-270651db6a7b%2Fu62wgh_processed.png&w=3840&q=75)
Transcribed Image Text:An epidemic spreads through a population at a rate proportional to the product of the number of people
already infected and the number of people susceptible, but not yet infected. Therefore, if S denotes the
total population of susceptible people and I = I(t) denotes the number of infected people at time t, then
I'= rI(S – I),
where r is a positive constant.
A) Let's say that there are 2000 susceptible people in a nursing home, so S = 2000. Let's also say that one
infected person visits the home, so that I(0) = 1.
Find the function I(t) for the number of peope infected at time t > 0.
I(t) =
=
B) If the infection rate is r = 0.0004, how many people are infected after t
please)
5 days? (Whole people only,
C) As the value of t increases, can you see what I(t) become? In other words, calculate the following limit
lim I(t) =
=
t→∞
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