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

question 62

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 $4$ 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) \(150.54 \text { months }\)

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