The fixed points of the logistic equation dP/dt = kP(1 - P/L) occur when P equals which values?

Study for the AP Calculus BC Test. Discover flashcards and multiple choice questions with hints and explanations to prepare effectively. Ace your exam!

Multiple Choice

The fixed points of the logistic equation dP/dt = kP(1 - P/L) occur when P equals which values?

Explanation:
Fixed points are values of P where the rate of change is zero. For dP/dt = kP(1 − P/L), set the right-hand side equal to zero. Since k ≠ 0, the product is zero when P = 0 or when 1 − P/L = 0, which gives P = L. So the equilibria are P = 0 and P = L. In a population model, P = 0 means extinction stays extinct, and P = L is the carrying capacity where growth stops.

Fixed points are values of P where the rate of change is zero. For dP/dt = kP(1 − P/L), set the right-hand side equal to zero. Since k ≠ 0, the product is zero when P = 0 or when 1 − P/L = 0, which gives P = L. So the equilibria are P = 0 and P = L. In a population model, P = 0 means extinction stays extinct, and P = L is the carrying capacity where growth stops.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy