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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 =

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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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: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
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.
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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