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

Multiple Choice

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 $k y ^ { 1.04 }$ . If 5 such rabbits breed initially and the warren has 23 rabbits after 5 months, then when is doomsday? Select the correct answer.

A) $138.06$ months
B) $158.06$ months
C) $118.06$ months
D) $88.06$ months
E) $68.06$ months