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Exponential Function - Exponential Decay Worksheet Answers

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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.

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