To determine the correct graph that displays the points for Cason's anesthetic metabolization, we can calculate the values of the function \( f(x) = 320(0.75)^x \) for \( x = 0, 1, 2, 3, 4, 5 \):
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For x = 0: \[ f(0) = 320(0.75)^0 = 320 \times 1 = 320 \text{ mg} \]
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For x = 1: \[ f(1) = 320(0.75)^1 = 320 \times 0.75 = 240 \text{ mg} \]
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For x = 2: \[ f(2) = 320(0.75)^2 = 320 \times 0.5625 = 180 \text{ mg} \]
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For x = 3: \[ f(3) = 320(0.75)^3 = 320 \times 0.421875 = 135 \text{ mg} \]
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For x = 4: \[ f(4) = 320(0.75)^4 = 320 \times 0.31640625 = 101.56 \text{ mg} \]
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For x = 5: \[ f(5) = 320(0.75)^5 = 320 \times 0.2373046875 = 75.38 \text{ mg} \]
Now we have the following points to plot:
- \( (0, 320) \)
- \( (1, 240) \)
- \( (2, 180) \)
- \( (3, 135) \)
- \( (4, 101.56) \)
- \( (5, 75.38) \)
Analyzing the Options:
Option #1: A decreasing curve plotted on a coordinate plane, with the x-axis for hours ranging from 0 to 7 (increments of 1), and the y-axis for milligrams ranging from 0 to 350 (increments of 50). This fits the values we calculated.
Option #2: A curve with an arrow at the top plotted with the x-axis for hours ranging from 0 to 350 and y-axis for milligrams from 0 to 7. This is not suitable as the axes do not correspond to the data we have.
Option #3: A decreasing curve plotted on a coordinate plane with the same axes as Option #1. This also fits the values we calculated.
Conclusion:
Both Options #1 and #3 correctly display the points derived from the function \( f(x) \). If you have to choose one option, you can choose either, but given the instruction to select only one, I would recommend:
The graph with the correct plotted points is Option #1.