See the graph below for its derivative.
Work Step by Step
The slope of the $P(t)$ graph is always positive, so it stays above the $t$-axis. But it varies at different points. The graph gets steepest at around $t=6$, so the slope increases until that point and then it decreases toward zero. The derivative of this graph shows us that as time passes by, the growth of the population approaches zero as it reaches a stable level.