A curve representing the total number of people, P, infected with a virus often has the shape of a logistic curve of the form 1+ Ce-kt with time t in weeks. Suppose that 12 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 6000 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 = 12, to find C.
A curve representing the total number of people, P, infected with a virus often has the shape of a logistic curve of the form 1+ Ce-kt with time t in weeks. Suppose that 12 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 6000 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 = 12, to find C.
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:(b) Use the fact that when \( t = 0 \), we have \( P = 12 \), to find \( C \).
*NOTE: Enter the exact answer.*
\( C = \underline{\hspace{3cm}} \)
(c) Now that you have estimated \( L \), \( k \), and \( C \), what is the logistic function you are using to model the data?
\( P(t) = \underline{\hspace{5cm}} \)
(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.*
\( t \approx \underline{\hspace{2cm}} \quad P \approx \underline{\hspace{2cm}} \)
![A curve representing the total number of people, \( P \), infected with a virus often has the shape of a logistic curve of the form
\[
P = \frac{L}{1 + Ce^{-kt}}
\]
with time \( t \) in weeks. Suppose that 12 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 6000 people will become infected.
(a) What should we use for the parameters \( k \) and \( L \)?
**NOTE:** Enter the exact answers.
\[ k = \quad \]
\[ L = \quad \]
(b) Use the fact that when \( t = 0 \), we have \( P = 12 \), to find \( C \).
**NOTE:** Enter the exact answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca5e629a-9287-4ec7-9b80-8449992c5732%2F8669211f-6518-45ac-991b-13a80f28ca34%2F9e2vhcp_processed.png&w=3840&q=75)
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
\[
P = \frac{L}{1 + Ce^{-kt}}
\]
with time \( t \) in weeks. Suppose that 12 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 6000 people will become infected.
(a) What should we use for the parameters \( k \) and \( L \)?
**NOTE:** Enter the exact answers.
\[ k = \quad \]
\[ L = \quad \]
(b) Use the fact that when \( t = 0 \), we have \( P = 12 \), to find \( C \).
**NOTE:** Enter the exact answer.
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