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Let cc Be a Positive Number dydt=ky1+c\frac { d y } { d t } = k y ^ { 1 + c }

question 19

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Let cc be a positive number. A differential equation of the form dydt=ky1+c\frac { d y } { d t } = k y ^ { 1 + c } where kk is a positive constant is called a doomsday equation because the exponent in the expression ky1+ck y ^ { 1 + c } is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term ky100k y ^ { 100 } . If 3 such rabbits breed initially and the warren has 27 rabbits after 3 months, then when is doomsday?

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