System Parameters
Interactive Analysis ($P_0$)
$\frac{dP}{dt} = kP(1 - \frac{P}{K})$
Initial Pop $P_0$ 200
TARGET INFLECTION ANALYSIS
Max Rate at $P =$ 500
Inflection Time $t =$ 2.77
LIMIT BEHAVIOR
$\lim_{t \to \infty} P(t) =$ 1000
Behavior: Drag $P_0$ above the carrying capacity $K$ and watch! The population cannot sustain itself, resulting in a negative derivative $\frac{dP}{dt} < 0$ that forces the population to exponentially decay down back to the $K$ asymptote!