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

question 59

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 $k y ^ { 103 }$ . 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

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