Solution Found!
Solved: PROBLEM 8E(a) Suppose a = b = 1 in the Gompertz
Chapter 3, Problem 8E(choose chapter or problem)
(a) Suppose a = b = 1 in the Gompertz differential equation (7). Since the DE is autonomous, use the phase portrait concept of Section 2.1 to sketch representative solution curves corresponding to the cases \(P_{0}>e \text { and } 0<P_{0}<e\).
(b) Suppose a = 1, b = 1 in (7). Use a new phase portrait to sketch representative solution curves corresponding to the cases \(P_{0}>e^{-1} \text { and } 0<P_{0}<e^{-1}\).
(c) Find an explicit solution of (7) subject to \(P(0)=P_{0}\).
Text Transcription:
P_0 > e and 0 < P_0 < e
P_0 > e^1 and 0 < P_0 < e^1.
P(0) = P_0
Questions & Answers
QUESTION:
(a) Suppose a = b = 1 in the Gompertz differential equation (7). Since the DE is autonomous, use the phase portrait concept of Section 2.1 to sketch representative solution curves corresponding to the cases \(P_{0}>e \text { and } 0<P_{0}<e\).
(b) Suppose a = 1, b = 1 in (7). Use a new phase portrait to sketch representative solution curves corresponding to the cases \(P_{0}>e^{-1} \text { and } 0<P_{0}<e^{-1}\).
(c) Find an explicit solution of (7) subject to \(P(0)=P_{0}\).
Text Transcription:
P_0 > e and 0 < P_0 < e
P_0 > e^1 and 0 < P_0 < e^1.
P(0) = P_0
ANSWER:Step 1 of 5
In this problem, we need to find the explicit solution of the equation and draw the graph using the phase portrait concept .
