A population P obeys the logistic model. It satisfies the equation dP 8 -P(9 - P) for P > 0. dt 900 (a) The population is increasing when 0 (b) The population is decreasing when P > 9 (c) Assume that P(0) = 3. Find P(68). P(68) = < P < 9
A population P obeys the logistic model. It satisfies the equation dP 8 -P(9 - P) for P > 0. dt 900 (a) The population is increasing when 0 (b) The population is decreasing when P > 9 (c) Assume that P(0) = 3. Find P(68). P(68) = < P < 9
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![A population \( P \) obeys the logistic model. It satisfies the equation
\[
\frac{dP}{dt} = \frac{8}{900}P(9-P) \quad \text{for} \quad P > 0.
\]
(a) The population is increasing when \( 0 < P < 9 \).
(b) The population is decreasing when \( P > 9 \).
(c) Assume that \( P(0) = 3 \). Find \( P(68) \).
\[ P(68) = \]
*This equation models how a population grows over time, influenced by both linear growth and a limiting factor that depends on the population size.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30a42a85-c58f-45ac-a4af-faeed1a599e1%2Fa9137c00-88e6-4d25-997e-f4b16d6b81bd%2F3mlpv4_processed.png&w=3840&q=75)
Transcribed Image Text:A population \( P \) obeys the logistic model. It satisfies the equation
\[
\frac{dP}{dt} = \frac{8}{900}P(9-P) \quad \text{for} \quad P > 0.
\]
(a) The population is increasing when \( 0 < P < 9 \).
(b) The population is decreasing when \( P > 9 \).
(c) Assume that \( P(0) = 3 \). Find \( P(68) \).
\[ P(68) = \]
*This equation models how a population grows over time, influenced by both linear growth and a limiting factor that depends on the population size.*
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