Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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![Assume 9 people originally have the virus and that in early stages the number of people infected is increasing approximately exponentially, with a continuous growth rate of 1.19. Assume further that in the long run, they estimate approximately 9000 people will be infected.
(You may wish to sketch a graph of your logistic function \( P = \frac{L}{1 + Ce^{-kt}} \) to help you understand this situation and answer the questions below.)
(a) What should we use for the parameters \( k \) and \( L \)?
\[ k = \]
\[ L = \]
(b) Use the fact that when \( t = 0 \), we have \( P = 9 \), to find \( C \).
\[ C = \]
(c) What is the value of \( P \) when the rate at which people are becoming infected peaks?
\[ P = \]
When does this occur?
\[ t = \]](https://content.bartleby.com/qna-images/question/0dcc51e9-e947-4215-91cf-9c9e09d6c1cf/71dd6a7a-3ffa-4fb3-a169-1f6eeff25d83/p7itq7f_processed.png)
Transcribed Image Text:Assume 9 people originally have the virus and that in early stages the number of people infected is increasing approximately exponentially, with a continuous growth rate of 1.19. Assume further that in the long run, they estimate approximately 9000 people will be infected.
(You may wish to sketch a graph of your logistic function \( P = \frac{L}{1 + Ce^{-kt}} \) to help you understand this situation and answer the questions below.)
(a) What should we use for the parameters \( k \) and \( L \)?
\[ k = \]
\[ L = \]
(b) Use the fact that when \( t = 0 \), we have \( P = 9 \), to find \( C \).
\[ C = \]
(c) What is the value of \( P \) when the rate at which people are becoming infected peaks?
\[ P = \]
When does this occur?
\[ t = \]
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- A rumor spreads through a school with 3000 students. At 8 AM, 120 students have heard the rumor, and by noon, half the school has heard it. Using the logistic model 1 y(t) p-kt 1 . B determine when 90% of the students will have heard the rumor. (Use decimal notation. Give your answer to one decimal place.) t = hoursarrow_forwardSolve b letter i to find the solution of the given problems.arrow_forwardAssume 100 snails originally have the virus and that in early stages the number of snails infected is increasing approximately exponentially, with a continuous growth rate of 0.02. Assume further that in the long run, they estimate approximately 5300 snails will be infected. The number of snails infected after t hours after infection began is modeled by a logistic function: P=L1+Ce−kt What is the value of t when the rate at which snails are becoming infected peaks? Select the closest value.arrow_forward
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