Lona received a stamp collection from her grandmother. The collection is in a leather book and currently has $120$ stamps. Lona joined a stamp club, which sends her $12$ new stamps each month. The stamp book holds a maximum of $500$ stamps.

1. Complete the table at right.

   Hint (a):

   Continue adding $12$ to find months $2-5$.

2. How many stamps will Lona have one year from now?

   Hint (b):

   Continue the table to month $12$.

3. Write an equation using function notation to represent the total number of stamps that Lona has in her collection after $n$ months. Let the total be represented by $t(n)$.

   Hint (c):

   Remember that the initial amount was $120$ stamps and the rate is $12$ stamps per month.

   Answer (c):

   $t(n)=120+12n$

4. Solve your equation from part (c) for $n$ when $t(n)=500$. Will Lona be able to fill her book exactly with no stamps remaining? How do you know? When will the book be filled?

   Hint (d):

   Substitute $500$ for $t(n)$.

   $500=120+12n$