2. Let c be a positive number. A differential equation of the form = ky¹+e, where k is a positive constant, is called a doomsday equation because the exponent in the expression ky¹+c is larger than the exponent 1 for natural growth. a) Determine the solution that satisfies the initial condition y(0) = yo. b) Show that there is a finite time t = T (doomsday) such that lim→T- y(t): = ∞. c) An especially prolific breed of rabbits has the growth term ky¹.01. If two such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?
2. Let c be a positive number. A differential equation of the form = ky¹+e, where k is a positive constant, is called a doomsday equation because the exponent in the expression ky¹+c is larger than the exponent 1 for natural growth. a) Determine the solution that satisfies the initial condition y(0) = yo. b) Show that there is a finite time t = T (doomsday) such that lim→T- y(t): = ∞. c) An especially prolific breed of rabbits has the growth term ky¹.01. If two such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?
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 1CR
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