The population of rabbits on a small island grows at a rate that is jointly

Question

The population  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  rabbits, which of the following differential equations best models the growth rate of the rabbit population with respect to time , where  is a constant?

dP/dt=2400-kP

dP/dt=k(2400-P)

dP/dt=k 1/p (2400-P)

dP/dt=kP(2400-P)

Answer 1

If "P" is the rabbit population then dP/dt is the population growth rate. The problem says the growth rate "dP/dt" varies jointly with the population "P" and the difference of the carrying capacity (I assume this is 2400) and the population (so 2400 - P).

Varies jointly means something is proportional to a product, like z varies jointly with x and y is z = kxy.

So dP/dt = kP(2400-P)