Question

A habitat of prairie dogs can support mmm dogs at most.

The habitat's population, ppp, grows proportionally to the product of the current population and the difference between mmm and ppp.

Which equation describes this relationship?

Answer 1

dP/dT = kp(m - p)

Answer 2

The correct answer is p = K × x × (m - p) , where K is the constant of proportionality and x is the current population of the habitat.

Explanation:

A habitat of prairie dogs can support m dogs at most.

Let us consider the current population of the habitat be x.

Given the condition that the habitat's population, p, grows proportionally to the product of the current population (x) and the difference between m and p.

Thus the proportional equation would look like:

p ∝ x × (m - p)

⇒ p = K × x × (m - p) , where K is the constant of proportionality.

Thus the equation describing the above mentioned relationship is given by the above equation.