An item currently costing $$20$ is increasing in cost by $5$% per year.

1. What is the multiplier?

   Hint (a):

   The cost is increasing, so the multiplier will be greater than $1$.

   Answer (a):

   $1.05$

2. What will the item cost five years from now?

   Hint (b):

   The original cost would be multiplied by $1.05$ for the first year, an additional $1.05$ for the second year, an additional $1.05$ every year after that.

   Answer (b):

   $$25.52$

3. Write an equation to calculate the cost in $n$ years. What does each of the factors in your equation represent?

   Hint (c):

   Use the starting value and multiplier to write an equation of the form $t(n) = ab^n$