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Suppose you wish to predict future values of some quantity, y, using an autonomous differential equation. Experiments have been performed that give the following information: • The only equilibrium solutions are y(t) = 0, y(t) = 15, and y(t) = 60 • If the value of y is 100, the quantity decreases • If the value of y is 30, the quantity increases • If the value of y is negative, the quantity increases %3D (a) How many different phase lines match the above? Sketch all possible phase lines. (b) Provide a rough sketch of an autonomous derivative graph for each of your phase lines in part 2a. (c) For each of your different sketches in part 2b, develop a differential equation that fits the basic features.

Suppose you wish to predict future values of some quantity, y, using an autonomous differential equation. Experiments have been performed that give the following information: • The only equilibrium solutions are y(t) = 0, y(t) = 15, and y(t) = 60 • If the value of y is 100, the quantity decreases • If the value of y is 30, the quantity increases • If the value of y is negative, the quantity increases %3D (a) How many different phase lines match the above? Sketch all possible phase lines. (b) Provide a rough sketch of an autonomous derivative graph for each of your phase lines in part 2a. (c) For each of your different sketches in part 2b, develop a differential equation that fits the basic features.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Answer all parts please. also for part A can you make sure its phase lines

Suppose you wish to predict future values of some quantity, y, using an autonomous differential equation. Experiments have been performed that give the following information: • The only equilibrium solutions are y(t) = 0, y(t) = 15, and y(t) = 60 • If the value of y is 100, the quantity decreases • If the value of y is 30, the quantity increases • If the value of y is negative, the quantity increases (a) How many different phase lines match the above? Sketch all possible phase lines. (b) Provide a rough sketch of an autonomous derivative graph for each of your phase lines in part 2a. (c) For each of your different sketches in part 2b, develop a differential equation that fits the basic features.
Transcribed Image Text:Suppose you wish to predict future values of some quantity, y, using an autonomous differential equation. Experiments have been performed that give the following information: • The only equilibrium solutions are y(t) = 0, y(t) = 15, and y(t) = 60 • If the value of y is 100, the quantity decreases • If the value of y is 30, the quantity increases • If the value of y is negative, the quantity increases (a) How many different phase lines match the above? Sketch all possible phase lines. (b) Provide a rough sketch of an autonomous derivative graph for each of your phase lines in part 2a. (c) For each of your different sketches in part 2b, develop a differential equation that fits the basic features.
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