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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
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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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
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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