Let(adsbygoogle = window.adsbygoogle || []).push({}); cbe a positive number. A differential equation of the form:dy/dt = ky^(1+c)

wherekis a positive constant, is called adoomsday equationbecause the equation in the expressionky^(1+c)is larger than that for natural growth (that is,ky).

(a) Determine the solution that satisfies the initial condition y(0)=y(subzero)

(b) Show that there is a finite timet = T(doomsday) such that lim(t->T-) y(t) = infinity

(c) An especially prolific breed of rabbits has the growth termky^(1.01). If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?

We just got finished learning Radioactive Decay and Newton's Law of Cooling sections which this question has come from and I have no idea even how to approach this such question.

Any help would be appreciated. Don't flat out give me the answer, but offer any positive assistance. Thanks!!

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# Doomsday Equation

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