Let c be a positive number. A differential equation of the form dy/dt = ky1+ewhere k is a positive constant, is called a doomsday equation becausethe exponent in the expression ky1+e is larger than the exponent 1fornatural growth.(a) Determine the solution that satisfies the initial condition y (0) = y0.•(b) Show that there is a finite time t=T (doomsday) such that limt→T -(t)=∞.(c) An especially prolific breed of rabbits has the growth term ky1.01 • If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?

Let c be a positive number. A differential equation of the form dy/dt = ky1+ewhere k is a positive constant, is called a doomsday equation becausethe exponent in the expression ky1+e is larger than the exponent 1fornatural growth.(a) Determine the solution that satisfies the initial condition y (0) = y0.•(b) Show that there is a finite time t=T (doomsday) such that limt→T -(t)=∞.(c) An especially prolific breed of rabbits has the growth term ky1.01 • If 2 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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