Problem (1) A population P is modeled by the differential dP = P(1- dt ). The slope field of the differential equation is 100 P equation shown below. 「本p II 250- 100 キ一メ 10\ 12 \14 V6 18 4\-ス \ LII I (i) Sketch the solution curves that satisfy the given initial conditions. P(0) = 100 P(0) = 50 P(0) = 200 (ii) What are the equilibrium solutions? (iii) For what values of P is the population increasing? Decreasing? (iv) Find lim P(t) for all P> 0.
Problem (1) A population P is modeled by the differential dP = P(1- dt ). The slope field of the differential equation is 100 P equation shown below. 「本p II 250- 100 キ一メ 10\ 12 \14 V6 18 4\-ス \ LII I (i) Sketch the solution curves that satisfy the given initial conditions. P(0) = 100 P(0) = 50 P(0) = 200 (ii) What are the equilibrium solutions? (iii) For what values of P is the population increasing? Decreasing? (iv) Find lim P(t) for all P> 0.
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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Transcribed Image Text:Problem (1) A population P is modeled by the differential
dP
= P(1-
dt
P
). The slope field of the differential equation is
equation
100
shown below.
3.
1.
1.
1.
3.
|| 250 +1
100 +
50
/////
+ +4 K44
\8\ 10\ 12 \14 16\ 18
41211 2
111 IIPI III II IT
(i) Sketch the solution curves that satisfy the given initial conditions.
P(0) = 100
P(0) = 50
P(0) = 200
(ii) What are the equilibrium solutions?
(iii) For what values of P is the population increasing? Decreasing?
(iv) Find lim P(t) for all P> 0.
t00
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