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(b) Use the fact that when t = 0, we have P = 10, 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 Pat this point? NOTE: Round your answer for t to one decimal place and your answer for P to the nearest hundred people. t≈ P≈

(b) Use the fact that when t = 0, we have P = 10, 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 Pat this point? NOTE: Round your answer for t to one decimal place and your answer for P to the nearest hundred people. t≈ P≈

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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(b) Use the fact that when t = 0, we have P = 10, 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 nearest hundred people. t≈ On P≈ D
Transcribed Image Text:(b) Use the fact that when t = 0, we have P = 10, 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 nearest hundred people. t≈ On P≈ D
A curve representing the total number of people, P, infected with a virus often has the shape of a logistic curve of the form L 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. P = (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. NOTE: Enter the exact answer. C
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 L 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. P = (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. NOTE: Enter the exact answer. C
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