A population grows according to the given logistic equation, where t is measured in weeks. dP dt = 0.05P-0.0025P2, P(0) = 16 (a) What is the carrying capacity? dP Using = KP dt P(t) = P M what is the value of k? (b) Write the solution of the equation. (c) What is the population after 15 weeks? (Round your answer to the nearest integer.) P(15) =
A population grows according to the given logistic equation, where t is measured in weeks. dP dt = 0.05P-0.0025P2, P(0) = 16 (a) What is the carrying capacity? dP Using = KP dt P(t) = P M what is the value of k? (b) Write the solution of the equation. (c) What is the population after 15 weeks? (Round your answer to the nearest integer.) P(15) =
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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![A population grows according to the given logistic equation, where \( t \) is measured in weeks:
\[
\frac{dP}{dt} = 0.05P - 0.0025P^2, \quad P(0) = 16
\]
### (a) What is the carrying capacity?
[Answer box]
Using \(\frac{dP}{dt} = kP \left(1 - \frac{P}{M}\right)\), what is the value of \( k \)?
[Answer box]
### (b) Write the solution of the equation.
\[ P(t) = \]
[Answer box]
### (c) What is the population after 15 weeks? (Round your answer to the nearest integer.)
\[ P(15) = \]
[Answer box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4acda8c7-3ed9-4816-93cd-e9a52e0b4613%2F2ac51c94-25cd-4966-8b83-0eb05be1c2dd%2F0kj18mm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A population grows according to the given logistic equation, where \( t \) is measured in weeks:
\[
\frac{dP}{dt} = 0.05P - 0.0025P^2, \quad P(0) = 16
\]
### (a) What is the carrying capacity?
[Answer box]
Using \(\frac{dP}{dt} = kP \left(1 - \frac{P}{M}\right)\), what is the value of \( k \)?
[Answer box]
### (b) Write the solution of the equation.
\[ P(t) = \]
[Answer box]
### (c) What is the population after 15 weeks? (Round your answer to the nearest integer.)
\[ P(15) = \]
[Answer box]
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