A model for the population P(t) in a suburb of a large city is given by the initial-value problem dp -). P(0) = 3000, dt -= 0.1 P(1 P 1000,000 where t is measured in months. The limiting value of the population and the time will take the population be equal to one-half of this limiting value respectively are a. 5000, b. 29.1 1000,000, 58.1 C. 2500, 85.1 d. 1000,000 55.5
A model for the population P(t) in a suburb of a large city is given by the initial-value problem dp -). P(0) = 3000, dt -= 0.1 P(1 P 1000,000 where t is measured in months. The limiting value of the population and the time will take the population be equal to one-half of this limiting value respectively are a. 5000, b. 29.1 1000,000, 58.1 C. 2500, 85.1 d. 1000,000 55.5
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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8.as soon as possible please
![**Population Dynamics in Urban Suburbs**
A model for the population \( P(t) \) in a suburb of a large city is given by the initial-value problem:
\[
\frac{dp}{dt} = 0.1 P\left(1 - \frac{P}{1000,000}\right), \quad P(0) = 3000,
\]
where \( t \) is measured in months.
The limiting value of the population and the time it will take for the population to be equal to one-half of this limiting value, respectively, are:
(a) 5000, 29.1
(b) 1000,000, 58.1
(c) 2500, 85.1
(d) 1000,000, 55.5
**Please select the correct answer:**
- \( \circ \) a
- \( \circ \) b
- \( \circ \) c
- \( \circ \) d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa72e8965-bd79-4464-a740-a72095a0be2c%2F5ba071b1-0a37-49e7-80b0-2b0ca77972ea%2Ff49sap2_processed.png&w=3840&q=75)
Transcribed Image Text:**Population Dynamics in Urban Suburbs**
A model for the population \( P(t) \) in a suburb of a large city is given by the initial-value problem:
\[
\frac{dp}{dt} = 0.1 P\left(1 - \frac{P}{1000,000}\right), \quad P(0) = 3000,
\]
where \( t \) is measured in months.
The limiting value of the population and the time it will take for the population to be equal to one-half of this limiting value, respectively, are:
(a) 5000, 29.1
(b) 1000,000, 58.1
(c) 2500, 85.1
(d) 1000,000, 55.5
**Please select the correct answer:**
- \( \circ \) a
- \( \circ \) b
- \( \circ \) c
- \( \circ \) d
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