The cost of a $55$ inch HDTV is decreasing $15\%$ per year.

1. What is the multiplier?

   Hint (a):

   If the cost decreased by $15\%$ each year, the newcost would be $85\%$ of the previous year.

   Answer (a):

   $0.85$

2. If the current cost of the HDTV is $$1500$, what will it cost in four years?

   Hint (b):

   In one year the cost will be $$1500\left(0.85\right)$.
   In two years the cost will be $$1500\left(0.85\right)]\left(0.85\right)$.
   Continue this pattern.

3. If the current cost of the HDTV is $$1500$, write an equation for the cost in $n$ years.

   Hint (c):

   Use the pattern in part (b) to write your equation.