Mathematics

The logistic model describes growth that starts slow, accelerates, then plateaus at a maximum capacity—called the carrying capacity. As $t \to \infty$, the exponential term $e^{-0.3t}$ shrinks to zero because you're raising a number less than 1 to an increasingly large power. Once that term vanishes, you're left with just the numerator divided by 1, which reveals the long-term equilibrium the population approaches.

The logistic model describes growth that starts slow, accelerates, then plateaus at a maximum capacity—called the carrying capacity. As $t \to \infty$, the exponential term $e^{-0.3t}$ shrinks to zero because you're raising a number less than 1 to an increasingly large power. Once that term vanishes, you're left with just the numerator divided by 1, which reveals the long-term equilibrium the population approaches.