The slope field for the equation dP/dt = 0.05P(20 - P), for P≥ 0, is shown below. For which positive values of P are the solutions increasing? Increasing for: P 1 For what positive values of P are the solutions decreasing? Decreasing for: 20 On a print out of this slope field, sketch the solutions that pass through (0, 0); (2,8); (8, 2); (−9.5, 2); (−4, 24); and (-4, 20). 20 (Give your answer as an interval or list of intervals, e.g., if P is increasing between 1 and 5 and between 7 and infinity, enter (1,5),(7,Inf).) (Again, give your answer as an interval or list of intervals, e.g., if P is decreasing between 1 and 5 and between 7 and infinity, enter (1,5),(7,Inf).) What is the equation of the solution to this differential equation that passes through (0,0)? P = If the solution passes through a value of P > 0, what is the limiting value of P as t gets large? P→→
The slope field for the equation dP/dt = 0.05P(20 - P), for P≥ 0, is shown below. For which positive values of P are the solutions increasing? Increasing for: P 1 For what positive values of P are the solutions decreasing? Decreasing for: 20 On a print out of this slope field, sketch the solutions that pass through (0, 0); (2,8); (8, 2); (−9.5, 2); (−4, 24); and (-4, 20). 20 (Give your answer as an interval or list of intervals, e.g., if P is increasing between 1 and 5 and between 7 and infinity, enter (1,5),(7,Inf).) (Again, give your answer as an interval or list of intervals, e.g., if P is decreasing between 1 and 5 and between 7 and infinity, enter (1,5),(7,Inf).) What is the equation of the solution to this differential equation that passes through (0,0)? P = If the solution passes through a value of P > 0, what is the limiting value of P as t gets large? P→→
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:The slope field for the equation dP/dt = 0.05P(20 — P), for P ≥ 0, is shown below.
For which positive values of P are the solutions increasing?
Increasing for:
P₁
On a print out of this slope field, sketch the solutions that pass through (0, 0); (2, 8); (8, 2); (−9.5, 2); (−4, 24);
and (-4, 20).
For what positive values of P are the solutions decreasing?
Decreasing for:
20
20
(Give your answer as an interval or list of intervals, e.g., if P is increasing between 1 and 5 and between 7 and infinity,
enter (1,5),(7,Inf).)
=
(Again, give your answer as an interval or list of intervals, e.g., if P is decreasing between 1 and 5 and between 7 and
infinity, enter (1,5),(7,Inf).)
What is the equation of the solution to this differential equation that passes through (0,0)?
P
If the solution passes through a value of P > 0, what is the limiting value of P as t gets large?
P→
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