The population of cook island was always been modeled by a logistic equation with growth rate r=19 and carrying capacity n=8000, with time t measured in years. however, beginning in 2000, 9 citizens of cook island have left every year to become a mathematician, never to return. find the new differential equation modeling the population of the island p(t) after 2000. use p for p(t) and p' for p′(t)
the answer is p' = p/9(1-p/8000)-9

Step-by-step explanation:

The logistic equation is given by Equation 1):

1)

In which P represents the population, is the variation of the population in function of time, r is the growth rate of the population and N is the carrying capacity of the population.

Now for your system:

The problem states that the population has growth rate r=19.

The problem also states that the population has carrying capacity N=8000.

We can replace these values in Equation 1), so:

However, beginning in 2000, 9 citizens of Cook Island have left every year to become a mathematician, never to return. So, we have to subtract these 9 citizens in the P'(t) equation. So:

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c