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

10-49.

The average cost of a movie ticket is $9.50. Homework Help ✎

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

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.

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

Solve for *x* (the number of years):

2(9.50) = 9.50(1.04)^{x}

≈ 17.67 years

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*?