To determine the correct option, we need to calculate the amount of anesthetic remaining in Cason's system at each hour (from 0 to 5) using the given function \( f(x) = 320(0.75)^x \).
Now we will calculate \( f(x) \):
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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 \( x = 3 \): \[ f(3) = 320(0.75)^3 = 320(0.421875) = 135 \]
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For \( x = 4 \): \[ f(4) = 320(0.75)^4 = 320(0.31640625) = 101.25 \approx 101 \]
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For \( x = 5 \): \[ f(5) = 320(0.75)^5 = 320(0.2373046875) = 75.36 \approx 75 \]
Now, we can summarize the amounts remaining at each hour:
| x (hours) | f(x) (mg) | |-----------|-----------| | 0 | 320 | | 1 | 240 | | 2 | 180 | | 3 | 135 | | 4 | 101 | | 5 | 75 |
Based on this data, the plotted points will show a decreasing trend as time increases, which suggests that the graph is decreasing.
Comparing this with the options:
- Option #1: This describes a decreasing curve, which matches our computed values.
- Option #2: This would not accurately reflect the situation since it suggests a curve increasing as milligrams go up with hours on the x-axis.
- Option #3: Also describes a decreasing curve, which matches our computed values.
Given that both Option #1 and Option #3 depict decreasing graphs, but with similar axis ranges, the correct answer would be:
The graph with the correct plotted points is Option #1.
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