P5, 40pts. Revisiting logistic growth. This problem considers the case where the logistic equation has a slowly varying carrying capacity k(et), where k is a smooth, positive function, but otherwise arbitrary. The equation is 3-(1-844)) y = ry k(et) where y(0) = a and r, a are positive constants. Obtain a first-term approximation of the solution valid for large t. For +10, attempt to determine the second term in the approximation.
P5, 40pts. Revisiting logistic growth. This problem considers the case where the logistic equation has a slowly varying carrying capacity k(et), where k is a smooth, positive function, but otherwise arbitrary. The equation is 3-(1-844)) y = ry k(et) where y(0) = a and r, a are positive constants. Obtain a first-term approximation of the solution valid for large t. For +10, attempt to determine the second term in the approximation.
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
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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