Let c be a positive number. A differential equation of the form
dy/dt = ky^(1+c)
where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^(1+c) is larger than that for natural growth (that is, ky).
It can be shown that there is a finite time t=T (doomsday) such that lim y(t)=infinity, as t approach T from the left.
An especially prolific breed of rabbits has the growth term ky^(1.01). If 2 such rabbits breed initially and the warren has 16 rabbits after four months, then when is doomsday?
Please round the answer to two decimal places.
Can someone explain this problem please?
dy/dt = ky^(1+c)
where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^(1+c) is larger than that for natural growth (that is, ky).
It can be shown that there is a finite time t=T (doomsday) such that lim y(t)=infinity, as t approach T from the left.
An especially prolific breed of rabbits has the growth term ky^(1.01). If 2 such rabbits breed initially and the warren has 16 rabbits after four months, then when is doomsday?
Please round the answer to two decimal places.
Can someone explain this problem please?