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**1. The problem statement, all variables and given/known data**

P: Let c be a positive number. A differential equation of the form: dy/dt = ky^(1+c)

where k is a positive constant, is called a doomsday equation because the equation in the expression ky^(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 time t = ta (doomsday) such that lim(t->T-) wy(t) = infinity

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

**2. Relevant equations**

integration

**3. The attempt at a solution**

First i wanted to find solution to the dy/dx (meaning i integrated it)

I got y^c = -c(kx+T)

but i could not define it as function y because of the negative sign in front of C

What should i do?