微分方程：逻辑模型应用题

一片草地上老鼠的总量 $P(t)$P, left parenthesis, t, right parenthesis 在 $t$t 年后满足逻辑微分方程 $\dfrac{dP}{dt}=3P\cdot\left(1-\dfrac{P}{2500} \right)$start fraction, d, P, divided by, d, t, end fraction, equals, 3, P, dot, left parenthesis, 1, minus, start fraction, P, divided by, 2500, end fraction, right parenthesis 其中初始数量为 $1000$1000 只老鼠.

只老鼠