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Suppose that a population develops according to the logistic equation dP dt = 0.02P-0.0002P², where t is measured in weeks. (a) What is the carrying capacity? M = 2x What is the value of k? k= 0.02 (b) A direction field for this equation is shown in the figure below. P 150 125 100 75 501 ✓ 25

Suppose that a population develops according to the logistic equation dP dt = 0.02P-0.0002P², where t is measured in weeks. (a) What is the carrying capacity? M = 2x What is the value of k? k= 0.02 (b) A direction field for this equation is shown in the figure below. P 150 125 100 75 501 ✓ 25

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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Suppose that a population develops according to the logistic equation dP dt = 0.02P-0.0002P², where t is measured in weeks. (a) What is the carrying capacity? M = 2x What is the value of k? k = 0.02 (b) A direction field for this equation is shown in the figure below. Р 150 125 100 75 501 25 \ || | PRAC
Transcribed Image Text:Suppose that a population develops according to the logistic equation dP dt = 0.02P-0.0002P², where t is measured in weeks. (a) What is the carrying capacity? M = 2x What is the value of k? k = 0.02 (b) A direction field for this equation is shown in the figure below. Р 150 125 100 75 501 25 \ || | PRAC
Where are the slopes close to D? (Enter your answers as a comma-separated list.) P-0,100 150 150 ✓ Where are the slopes largest? (Enter your answers as a comma-separated list.) P-100 100 (c) Use the direction field to sketch solutions for initial populations of 20, 40, 60, 80, 120, and 140. x Which solutions are increasing? (Enter your answer using interval notation.) Pos Which solutions are decreasing? (Enter your answer using interval notation.) Po 150 Show Transcribed Text (c) Use the direction field to sketch solutions for initial populations of 20, 40, 60, 80, 120, and 140 P Ű 100 130 100 50 Y 100
Transcribed Image Text:Where are the slopes close to D? (Enter your answers as a comma-separated list.) P-0,100 150 150 ✓ Where are the slopes largest? (Enter your answers as a comma-separated list.) P-100 100 (c) Use the direction field to sketch solutions for initial populations of 20, 40, 60, 80, 120, and 140. x Which solutions are increasing? (Enter your answer using interval notation.) Pos Which solutions are decreasing? (Enter your answer using interval notation.) Po 150 Show Transcribed Text (c) Use the direction field to sketch solutions for initial populations of 20, 40, 60, 80, 120, and 140 P Ű 100 130 100 50 Y 100
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