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.