To complete the chart based on the exponential equation \( f(x)=320(0.75)^x \), we need to calculate the values of \( f(x) \) for \( x \) values from 0 to 5.
Given \( f(x) = 320(0.75)^x \):
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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 \( x = 4 \): \[ f(4) = 320(0.75)^4 = 320(0.31640625) \approx 101.25 \]
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For \( x = 5 \): \[ f(5) = 320(0.75)^5 = 320(0.2373046875) \approx 75.00 \]
Now, we can summarize the values:
| x | f(x) | |-----|--------| | 0 | 320 | | 1 | 240 | | 2 | 180 | | 3 | 135 | | 4 | 101.25| | 5 | 75 |
Thus, the completed chart is:
- For \( x = 0 \), \( f(x) = 320 \)
- For \( x = 1 \), \( f(x) = 240 \)
- For \( x = 2 \), \( f(x) = 180 \)
- For \( x = 3 \), \( f(x) = 135 \)
- For \( x = 4 \), \( f(x) = 101.25 \)
- For \( x = 5 \), \( f(x) = 75 \)
You can now plot the points based on this table to determine which graph correctly represents this decay.
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