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 with the answers to Exponential Function - Exponential Decay Worksheet.

### 1. Initial Amount

What was the initial amount of weekly 2-D movie attendance (*a*)?

240,000 patrons

### 2. Decay Factor

What is the decay factor (*b*)?

.05 (5 percent as a decimal)

### 3. Write the Function

Write a function describing the decline of 2-D movie attendance. Hint: *y* = *a(1 -b) ^{x}*

*y* = 240,000(1 - .05)^{x}

### 4. Predictions

A. Based on the function, predict the weekly 2-D movie attendance in Week 7.

*y* = 240,000(1 - .05)^{x}

*y* = 240,000(.95)^{7}

*y* = 240,000 * .698

*y* = 167,600.955

**About 167,601 people will attend the 2-D movies in Week 7.**

B. Based on the function, when will the weekly 2-D movie attendance fall below 10,000?

*y* = 240,000(1 - .05)^{x}

*Hint: Guess and test until you get the answer:*

**1. Is it the 17th week?**

*y* = 240,000(1 - .05)^{x}

*y* = 240,000(1 - .05)^{17}

y = 100,349 people

**2. Is it the 18th week?**

*y* = 240,000(1 - .05)^{x}

*y* = 240,000(1 - .05)^{18}

y = 95,331 people

Between Weeks 17 and 18, weekly attendance for 2-D films will fall below 100,000.