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# Exponential Function - Exponential Decay Worksheet

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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.

Check your answers.

### 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?

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