In the lotka-volterra predator-prey model dx/dt=-ax+bxy,dy/dt=ey-cxy, where x(t) is the predator population and y(t) is the prey population, the coefficient c represents which of the following: a) the predator die-off rateb) the prey growth ratec) the increase in the predator population due to interactions with the preyd) the decrease in the prey population due to interactions with the predator

D) the decrease in the prey population due to interactions with the predator

Step-by-step explanation:

We have that:

x is the predator population

y is the prey population.

The coefficient c appears in the equation of dy/dt. So this coefficient is related to the population of the prey. It appears with a minus sign, this means that the prey population decreases. It also multiplies x, so it means that it is related to the predator population.

The correct answer is:

D) the decrease in the prey population due to interactions with the predator

See Explanation

Step-by-step explanation:

Given

Required

Why dividing by is not reliable

The reason is that, the given expression is a quadratic equation and as such, it will most likely have two solutions.

So, when the expression is divided by , the solution will be , leaving out the other possible solution.

The right way is:

Subtract 6x from both sides

Factorize

Split

Solve for x in both cases: