The 3-D movie is emerging from its humble origins of hokey Disney Land films (see Michael Jackson’s Captain Eo) and educational IMAX films. Now, 3-D is for the average popcorn gorging, butter adding, diet cola swilling movie goer. All hail King James Cameron. He directed Avatar, the wildly popular – and profitable - 3-D film.
Every weekend, it seems like a new movie opens to audiences wearing 3-D glasses. What will happen to conventional 2-D movies? I’m not a mind reader, but I speculate that Hollywood will follow the profits. More 3-dimensional films and fewer 2-dimensional films are coming to a theater near you.
1. Exponential Decay Practice
This decline of the traditional film can be expressed by exponential decay.
Lodestar Theater shows 2-D and 3-D movies. Once the movie house began showing 3-D movies, audiences at 2-D movies have dwindled. The week before the debut of 3-D movies, 240,000 patrons watched 2-D movies. Every week since the debut, 2-D movie attendance has declined by 5 percent each week.
Use this information to answer the following questions about exponential decay.
2. Initial Amount
What was the initial amount of weekly 2-D movie attendance (a)?
3. Decay Factor
What is the decay factor (b)?
4. Write the Function
Write a function describing the decline of 2-D movie attendance. Hint: y = a(1 -b)x
5. Predictions
A. Based on the function, predict the weekly 2-D movie attendance in Week 7.
B. Based on the function, when will the weekly 2-D movie attendance fall below 10,000?