Given: dP = 0.3(1-2)(− 1)P, where P(t) is population at time t. dt
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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Question
DRAW THE SOLUTION CURVE P(t) that satisfies the initial condition P(0)=75
NOTE: I need a GRAPH, not for you to solve the equation.
![The equation presented is:
\[
\frac{dP}{dt} = 0.3 \left(1 - \frac{P}{200}\right)\left(\frac{P}{50} - 1\right)P
\]
where \( P(t) \) represents the population at time \( t \).
This differential equation describes the rate of change of a population over time. The equation takes into account factors that might limit the population, such as resources or environmental constraints, reflected in the terms \( \left(1 - \frac{P}{200}\right) \) and \( \left(\frac{P}{50} - 1\right) \). The constant \( 0.3 \) represents the growth rate factor.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d0ee2cb-cfe2-4eb9-a097-d38324436758%2Fbb00ed3d-9890-4779-ae8d-b7c718a033f4%2F4efhw0s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The equation presented is:
\[
\frac{dP}{dt} = 0.3 \left(1 - \frac{P}{200}\right)\left(\frac{P}{50} - 1\right)P
\]
where \( P(t) \) represents the population at time \( t \).
This differential equation describes the rate of change of a population over time. The equation takes into account factors that might limit the population, such as resources or environmental constraints, reflected in the terms \( \left(1 - \frac{P}{200}\right) \) and \( \left(\frac{P}{50} - 1\right) \). The constant \( 0.3 \) represents the growth rate factor.
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