Question

The population P of rabbits on a small island grows at a rate that is jointly proportional to the size of the rabbit population and the difference between the rabbit population and the carrying capacity of the population. If the carrying capacity of the population is 2400 rabbits, which of the following differential equations best models the growth rate of the rabbit population with respect to time t, where k is a constant?
(A) = 2400 - kps
(B) = k (2400 – P)
(C) = k 1/p (2400 – P)
(D) = XP (2400 - P)

Answer 1

Answer:

Option D:

$\frac{dP}{dt} = kP(2400 - P)$

Step-by-step explanation:

Differential equation:

For the population in function of the time, is:

$\frac{dP}{dt}$

The population P of rabbits on a small island grows at a rate that is jointly proportional to the size of the rabbit population and the difference between the rabbit population and the carrying capacity of the population

Carring capacity is 2400.

This means that the differential equation is kP(size of the population multiplied by the constant) multiplied by 2400 - P(difference between the population and the carrying capacity). So

$\frac{dP}{dt} = kP(2400 - P)$

So the answer is given by option D.