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

question 125

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 1 for natural growth. An especially prolific breed of rabbits has the growth term $k y ^ { 102 }$ . If 7 such rabbits breed initially and the warren has 21 rabbits after 8 months, then when is doomsday?

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