A small town's expansion is modeled by the function $S\left(t\right)=-\frac{1}{40}{t}^2+3t+15$, for $0 ≤ t ≤ 60$, where $S$ represents the area in square kilometers and $t$ is the number of years since $2000$. If the population density remains steady at $800$ people per square kilometer, what is the population growth rate in $2025$?