Mathematics · Differential Equations
Consider the prey population growth equation in a predator-prey model: du/dt = a·u(1 - u/k) - b·u·v, where u and v are prey and predator densities, respectively. The parameters a, b, and k are positive real numbers representing the intrinsic growth rate of u, the rate at which the predator v consumes u, and the carrying capacity. Which statement is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1In the absence of predators, the prey population grows exponentially indefinitely.
- 2The term 'b·u·v' represents the natural death rate of the prey population.
- 3The prey population remains constant over time, unaffected by predators.
- 4In the absence of predators, the prey population grows exponentially at first, then its growth slows down as it approaches k.✓
Correct answer
In the absence of predators, the prey population grows exponentially at first, then its growth slows down as it approaches k.
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