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Question

Part 1
A solid waste disposal plan proposes to reduce the amount of garbage each person throws out by 5​% each year. This​ year, each person threw out an average of 1700 lb of garbage. The function y equals 1700 times 0.95 Superscript x models the average amount of garbage each person will throw out each year after x years. Graph the function.
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Part 1
Choose the correct graph on the right.
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Part 1
A.
0
6
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3000
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y

x y graph
B.
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30
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2400
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y

x y graph
C.
0
6
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3000
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y

Answer 1

To graph the function \( y = 1700 \times 0.95^x \), we can analyze its behavior over a couple of years:

1. When \( x = 0 \): \[ y = 1700 \times 0.95^0 = 1700 \times 1 = 1700 \]

2. When \( x = 1 \): \[ y = 1700 \times 0.95^1 = 1700 \times 0.95 = 1615 \]

3. When \( x = 2 \): \[ y = 1700 \times 0.95^2 = 1700 \times 0.9025 = 1534.25 \]

4. When \( x = 3 \): \[ y = 1700 \times 0.95^3 = 1700 \times 0.857375 \approx 1457.53 \]

5. When \( x = 4 \): \[ y = 1700 \times 0.95^4 = 1700 \times 0.81450625 \approx 1384.61 \]

6. When \( x = 5 \): \[ y = 1700 \times 0.95^5 = 1700 \times 0.7737809375 \approx 1315.43 \]

When graphing, you'll want to observe that as \( x \) increases, \( y \) decreases steadily but more slowly because of the compounding percentage decrease.

Since we don't have the actual graphs to view, here's a guideline:

• Look for a graph that starts around 1700 for \( x = 0 \).
• Ensure that the values decrease over time, getting closer to zero but never quite reaching it, indicating an exponential decay pattern.
• The y-axis should be scaled appropriately to accommodate values starting from 1700 down to values closer to zero over several years.

Check the provided graph options for these characteristics to choose the correct graph that represents \( y = 1700 \times 0.95^x \).