A rate of increase in a population P is proportional to the square of the current population. Which differential equation could be used to model this situation?

dP/dt=kt^2
dP/dt=kP^2
dP/dt=kt
dP/dt=kP

Question

A rate of increase in a population P is proportional to the square of the current population. Which differential equation could be used to model this situation? 


dP/dt=kt^2 
dP/dt=kP^2 
dP/dt=kt 
dP/dt=kP

anonymous · Answer

Since the question asks about rate of population change, the two variables listed in the solutions are P, population, and t, time, so dP/dt is change in population over change in time.  Since the rate is proportional to the square of the population, it equals P^2 times some constant.  So, the correct answer is the second choice: dP/dt = kP^2