Lexington High School has an annual growth rate of $4.7\%$. Three years ago there were $1500$ students at the school.

1. How many students are there now?

   Hint (a):

   What is the multiplier? What is the initial value? Since you have information about $3$ years ago, what value of $n$ represents now?

   More Help (a):

   $f(n) = 1500(1.047)^n$

   Answer (a):

   $1722$

2. How many students were there $5$ years ago?

   Hint (b):

   $5$ years ago is $2$ years before there were $1500$ students. When were there $1500$ students? What would $n$ equal then?

   Answer (b):

   $1368$

3. How many students will there be $n$ years from now?

   Hint (c):

   Look back at the equation you used in part (a). What did the $3$ represent?
   How can you represent $n$ years from now in that equation?

   Answer (c):

   $y=1500(1.047)^{n + 3}$