Calc 2: Doomsday for Rabbit Population

[tnutty]

Let c be a positive number. A differential equation of the form below where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^(1+c) is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term ky1.01. If 3 such rabbits breed initially and the warren has 26 rabbits after three months, then when is doomsday? (Doomsday is the finite time t=T such that lim T->inf. Round the answer to two decimal places.)

dy/dt = ky^(1+c)

___months


attempt :

1/y^(1+c) dy = k dt

integrate both sides :

int [ ( 1/y^(1+c) ) ] = kt

not sure how to integrate the left side.

 

[tiny-tim]

int [ ( 1/y^(1+c) ) ] = kt

not sure how to integrate the left side.

Hi tnutty!

but it's just ∫ y^-n dy