Let c be a positive number. A differential equation of the form dy
dt= ky1 + c
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) = y0.
(b) Show that there is a finite time
t = T
(doomsday) such that
lim t %u2192 T%u2212y(t) = infinity.
(c) An especially prolific breed of rabbits has the growth term ky1.01. If 3 such rabbits breed initially and the warren has 24 rabbits after three months, then when is doomsday? (Round your answer to two decimal places.)