Question

The population of Cook island has always been modeled by a logistic equation P′=????(????−P) with growth rate ????=4 and carrying capacity ????=9000 with time t in years. Starting in 2000, 4 citizens of Cook island have left every year to become a mathematician, never to return.
What is the new differential equation modeling the population of the island P?

Answer 1

Answer:

$P = Ke^{(ln Pr^{c}-t) }$

Step-by-step explanation:

The differential equation is modeled as follows:

P = r (C-P)

then

$\frac{dP}{dt} = r(C-P)$

arranging gives:

$dP = Cr - Pr$

Arranging the equation gives:

$\frac{dP}{P} = \frac{C}{P}r - 1$

solving:

$P = e^{(lnPr^{c} -t)} K\\P = Ke^{(lnPr^{c} -t) }$