To find which graph displays the correct plotted points for the situation where Cason is given 320 milligrams of the anesthetic that metabolizes at a rate of 25% per hour, we can calculate the values of the function \( f(x) = 320(0.75)^x \) for \( x = 0, 1, 2, 3, 4, 5 \).
Here are the calculations:
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For \( x = 0 \): \( f(0) = 320(0.75)^0 = 320 \)
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For \( x = 1 \): \( f(1) = 320(0.75)^1 = 320 \times 0.75 = 240 \)
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For \( x = 2 \): \( f(2) = 320(0.75)^2 = 320 \times 0.5625 = 180 \)
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For \( x = 3 \): \( f(3) = 320(0.75)^3 = 320 \times 0.421875 = 135 \)
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For \( x = 4 \): \( f(4) = 320(0.75)^4 = 320 \times 0.31640625 \approx 101.25 \)
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For \( x = 5 \): \( f(5) = 320(0.75)^5 = 320 \times 0.2373046875 \approx 75.0 \)
This results in the following points plotted against hours (x-values):
- \( (0, 320) \)
- \( (1, 240) \)
- \( (2, 180) \)
- \( (3, 135) \)
- \( (4, 101) \)
- \( (5, 75) \)
The values show that the function decreases over time, starting at 320 milligrams and going down with each passing hour.
Now looking at the options given:
- Option #1 has a decreasing curve with correct axes for hours and milligrams.
- Option #2 seems incorrectly oriented, as it has hours on the y-axis and milligrams on the x-axis.
- Option #3 is the same as Option #1.
Thus, the correct graph with the plotted points is Option #1 (or #3, as they are effectively the same).
So the final answer is: The graph with the correct plotted points is Option #1.