Two bacterial cultures follow logistic models with the same growth rate but different…

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

Two bacterial cultures follow logistic models with the same growth rate

r=0.6

but different carrying capacities: Culture A:

\dfrac{dy}{dt}=0.6y(800-y)

, Culture B:

\dfrac{dv}{dt}=0.6v(1200-v)

. Both begin with 50 cells. Identify which culture will have the larger limiting population as

t\to\infty

, and state that limiting value.