Solution Found!
Use a sketch of the phase line (see Group Project C,
Chapter 3, Problem 11E(choose chapter or problem)
Use a sketch of the phase line (see Group Project C, Chapter 1) to argue that any solution to the logistic model
\(\frac{d p}{d t}=(a-b p) p ;\ \ p\left(t_{0}\right)=p_{0}\),
where 𝑎, 𝑏, and \(p_{0}\) are positive constants, approaches the equilibrium solution as \(p(t) \equiv a / b\) as 𝑡 approaches \(+\infty\).
Equation Transcription:
Text Transcription:
{dp}over{dt}=(a-bp)p; p(t_{0})=p_{0}
p_{0}
p(t) equiv a/b
+infinity
Questions & Answers
QUESTION:
Use a sketch of the phase line (see Group Project C, Chapter 1) to argue that any solution to the logistic model
\(\frac{d p}{d t}=(a-b p) p ;\ \ p\left(t_{0}\right)=p_{0}\),
where 𝑎, 𝑏, and \(p_{0}\) are positive constants, approaches the equilibrium solution as \(p(t) \equiv a / b\) as 𝑡 approaches \(+\infty\).
Equation Transcription:
Text Transcription:
{dp}over{dt}=(a-bp)p; p(t_{0})=p_{0}
p_{0}
p(t) equiv a/b
+infinity
ANSWER:
Solution
Step 1
In this problem, we have to stretch the the phase line and argue that any logistic model it approaches the equilibrium solution.