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 $k y ^ { 1.04 }$ . If $4$ such rabbits breed initially and the warren has $21$ rabbits after $8$ months, then when is doomsday?

A) $100.54 \text { months }$
B) $190.54 \text { months }$
C) $170.54 \text { months }$
D) $120.54 \text { months }$
E) $150.54 \text { months }$

Correct Answer:

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