A small town in Idaho has been growing exponentially. In $2019$ the town had $450$ people and in $2021$ the population had grown to $2,400$ people. Let $A(t)$ represent the number of people after $t$ years. Find the formula for $A(t),$ then find $A^{\text{'}}(4)$ and explain its meaning. Hint: $A=P{e}^{rt}$