Let $c$ Be a Positive Number $$\frac { d y } { d t } = k y ^ { 1 + c }$$

Let $c$ be a positive number. A differential equation of the form
$$\frac { d y } { d t } = k y ^ { 1 + c }$$
where $k$ is a positive constant is called a doomsday equation because the exponent in the expression $k y ^ { 1 + c }$ is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term $k y ^ { 1.03 }$ . If 3 such rabbits breed initially and the warren has 28 rabbits after 5 months, then when is doomsday?

A) $127.15$ months
B) $97.15$ months
C) $77.15$ months
D) $147.15$ months
E) $167.15$ months