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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
Related questions
Question
Transcribed Image Text:(b) Use the fact that when t = 0, we have P = 12, to find C.
NOTE: Enter the exact answer.
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
пеarest hundred people.
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 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
(b) Use the fact that when t = 0, we have P = 12, to find C.
NOTE: Enter the exact answer.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage