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

question 34

Short Answer

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 1for natural growth. An especially prolific breed of rabbits has the growth term $k y ^ { 106 }$ . If $5$ such rabbits breed initially and the warren has $25$ rabbits after $5$ months, then when is doomsday?

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