### Home > INT3 > Chapter 10 > Lesson 10.1.3 > Problem10-49

10-49.

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?

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

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

$≈ 17.67$ 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.

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 $y$?