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

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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.

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