The slope field for the equation dP/dt = 0.0333333P(30 – P), for P≥ 0, is shown below. Pl 11 1 1 1 1 1 1 1 1 38/11/1 717171717 212121}]} 30 On a print out of this slope field, sketch the solutions that pass through (0, 0); (3, 12); (12, 3); (−14.5, 3); (−6, 36); and (−6, 30). For which positive values of P are the solutions increasing? Increasing for: (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).) For what positive values of P are the solutions decreasing? Decreasing for: (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 = 0.0333333P(30 – P), for P≥ 0, is shown below. Pl 11 1 1 1 1 1 1 1 1 38/11/1 717171717 212121}]} 30 On a print out of this slope field, sketch the solutions that pass through (0, 0); (3, 12); (12, 3); (−14.5, 3); (−6, 36); and (−6, 30). For which positive values of P are the solutions increasing? Increasing for: (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).) For what positive values of P are the solutions decreasing? Decreasing for: (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→
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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Transcribed Image Text:0.0333333P(30 ) – P), for P ≥ 0, is shown below.
P
1 1
The slope field for the equation dP/dt =
1
1
30
30
On a print out of this slope field, sketch the solutions that pass through (0, 0); (3, 12); (12, 3); (−14.5, 3); (−6, 36); and (–6, 30).
For which positive values of P are the solutions increasing?
Increasing for:
(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).)
For what positive values of P are the solutions decreasing?
Decreasing for:
(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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