The average cost of a movie ticket is $$9.50$.

1. If the cost is increasing $4\%$ per year, in how many years will the cost double?

   Hint (a):

   Construct a representation of this scenario using the generic exponential equation:
   $y = ab^{x}$

   More Help (a):

   Solve for $x$ (the number of years):
   $2\left(9.50\right) = 9.50\left(1.04\right)^{x}$

   Answer (a):

   $≈ 17.67$ years

2. What is the average rate of change of the cost of a movie ticket over the interval of the next $10$ years? Explain what the average rate of change means in this context.

   Hint (b):

   The average rate of change is the same as asking for the slope of a line.
   What is the equation for slope, if the price is $x$ and time is $y$?