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

question 8

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 $k y ^ { 106 }$ . If 3 such rabbits breed initially and the warren has 27 rabbits after 3 months, then when is doomsday?

• A) \(47.03\) months
• B) \(97.03\) months
• C) \(67.03\) months
• D) \(137.03\) months
• E) \(117.03\) months

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