A curve representing the total number of people, P, infected with a virus often has the shape of a logistic curve of the form P - 1+ Ce-kt with time t in weeks. Suppose that 10 people originally have the virus and that in the early stages the number of people infected is increasing approximately exponentially, with a continuous growth rate of 1.78. It is estimated that, in the long-run, approximately 5000 people will become infected. (a) What should we use for the parameters k and NOTE: Enter the exact answers. L =
A curve representing the total number of people, P, infected with a virus often has the shape of a logistic curve of the form P - 1+ Ce-kt with time t in weeks. Suppose that 10 people originally have the virus and that in the early stages the number of people infected is increasing approximately exponentially, with a continuous growth rate of 1.78. It is estimated that, in the long-run, approximately 5000 people will become infected. (a) What should we use for the parameters k and NOTE: Enter the exact answers. L =
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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Transcribed Image Text:A curve representing the total number of people, P, infected with a
virus often has the shape of a logistic curve of the form
P =
1+ Ce-kt
with time t in weeks. Suppose that 10 people originally have the virus
and that in the early stages the number of people infected is increasing
approximately exponentially, with a continuous growth rate of 1.78. It
is estimated that, in the long-run, approximately 5000 people will
become infected.
(a) What should we use for the parameters k and L?
NOTE: Enter the exact answers.
k =
L =
(b) Use the fact that when t = 0, we have P = 10, to find C.
APR 6
étv
Transcribed Image Text:C =
(c) Now that you have estimated L, k, and C, what is the logistic
function you are using to model the data?
P(t) =
(d) Estimate the length of time until the rate at which people are
becoming infected starts to decrease. What is the value of P at
this point?
NOTE: Round your answer for t to one decimal place and your answer for P to the
nearest hundred people.
2
S 1 O 7 A
5
APR 6
étv J
280
t.
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