Another model for a growth function for a limited population is given by the Gompertz function, which is a solution to the differential equation 2. With c = € 0.05, Limit: dP dt K = where c is a constant and K is the carrying capacity. Answer the following questions. = = 4000, and 1. Solve the differential equation with a constant c = 0.05, carrying capacity K initial population Po = 1000. Answer: P(t) = || 4000, and Po = = cln (K) P 1000, find lim P(t). t→∞
Another model for a growth function for a limited population is given by the Gompertz function, which is a solution to the differential equation 2. With c = € 0.05, Limit: dP dt K = where c is a constant and K is the carrying capacity. Answer the following questions. = = 4000, and 1. Solve the differential equation with a constant c = 0.05, carrying capacity K initial population Po = 1000. Answer: P(t) = || 4000, and Po = = cln (K) P 1000, find lim P(t). t→∞
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Another model for a growth function for a limited population is given by the Gompertz function, which is a solution to the differential equation
\[
\frac{dP}{dt} = c \ln\left(\frac{K}{P}\right) P
\]
where \( c \) is a constant and \( K \) is the carrying capacity. Answer the following questions.
1. Solve the differential equation with a constant \( c = 0.05 \), carrying capacity \( K = 4000 \), and initial population \( P_0 = 1000 \).
Answer: \( P(t) = \) [Input box]
2. With \( c = 0.05 \), \( K = 4000 \), and \( P_0 = 1000 \), find \(\lim\limits_{t \to \infty} P(t)\).
Limit: [Input box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30a42a85-c58f-45ac-a4af-faeed1a599e1%2F64b0d8d4-cb9c-4254-8e3d-2ab530c0ffc3%2F7nenel9_processed.png&w=3840&q=75)
Transcribed Image Text:Another model for a growth function for a limited population is given by the Gompertz function, which is a solution to the differential equation
\[
\frac{dP}{dt} = c \ln\left(\frac{K}{P}\right) P
\]
where \( c \) is a constant and \( K \) is the carrying capacity. Answer the following questions.
1. Solve the differential equation with a constant \( c = 0.05 \), carrying capacity \( K = 4000 \), and initial population \( P_0 = 1000 \).
Answer: \( P(t) = \) [Input box]
2. With \( c = 0.05 \), \( K = 4000 \), and \( P_0 = 1000 \), find \(\lim\limits_{t \to \infty} P(t)\).
Limit: [Input box]
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