To fill in the remaining values of the chart using the given function \( f(x) = 320(0.75)^x \), we can calculate the amount of anesthetic remaining after each hour from \( x = 0 \) to \( x = 5 \).
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Calculate \( f(0) \): \[ f(0) = 320(0.75)^0 = 320(1) = 320 , \text{mg} \]
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Calculate \( f(1) \): \[ f(1) = 320(0.75)^1 = 320(0.75) = 240 , \text{mg} \]
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Calculate \( f(2) \): \[ f(2) = 320(0.75)^2 = 320(0.5625) = 180 , \text{mg} \]
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Calculate \( f(3) \): \[ f(3) = 320(0.75)^3 = 320(0.421875) = 135 , \text{mg} \]
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Calculate \( f(4) \): \[ f(4) = 320(0.75)^4 = 320(0.31640625) \approx 101 , \text{mg} \]
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Calculate \( f(5) \): \[ f(5) = 320(0.75)^5 = 320(0.2373046875) \approx 76 , \text{mg} \]
Now we can compile the values into the table:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline 0 & 320 \ 1 & 240 \ 2 & 180 \ 3 & 135 \ 4 & 101 \ 5 & 76 \ \hline \end{array} \]
Now, let's summarize the points to plot:
- (0, 320)
- (1, 240)
- (2, 180)
- (3, 135)
- (4, 101)
- (5, 76)
Given that the x-axis for hours ranges from 0 to 7 in increments of 1 and the y-axis for milligrams ranges from 0 to 350 in increments of 50, we can check for the graph that best represents a decreasing curve with these points.
The correct answer is Option #1 or Option #3 because they both describe a decreasing curve that fits the expected model. Since both Options 1 and 3 describe a decreasing curve, either could represent the data correctly.
So, the final answer is:
The graph with the correct plotted points is Option #1 or Option #3.
1 answer