To complete the chart based on the exponential function \( f(x) = 320(0.75)^x \), we can calculate the values of \( f(x) \) for each \( x \) value provided in the table.
Here’s how the calculations work for each \( x \):
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For \( x = 0 \): \[ f(0) = 320(0.75)^0 = 320(1) = 320 \]
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For \( x = 1 \): \[ f(1) = 320(0.75)^1 = 320(0.75) = 240 \]
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For \( x = 2 \): \[ f(2) = 320(0.75)^2 = 320(0.5625) = 180 \]
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For \( x = 3 \): \[ f(3) = 320(0.75)^3 = 320(0.421875) \approx 135 \]
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For \( x = 4 \): \[ f(4) = 320(0.75)^4 = 320(0.31640625) \approx 101 \]
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For \( x = 5 \): \[ f(5) = 320(0.75)^5 = 320(0.2373046875) \approx 76 \]
Now, the completed table should look like this:
| x | f(x) | |---|--------| | 0 | 320 | | 1 | 240 | | 2 | 180 | | 3 | 135 | | 4 | 101 | | 5 | 76 |
With these values, you can compare the points (0, 320), (1, 240), (2, 180), (3, 135), (4, 101), and (5, 76) to each of the graph options provided (Option #1, #2, #3) to find out which graph contains all of these plotted points.
Based on this analysis, identify the graph that matches the plotted points correctly.