To complete the chart for Cason’s anesthesia, you can use the exponential equation given:
\[ f(x) = 320(0.75)^x \]
Where \( x \) represents the number of hours after Cason receives the anesthetic. You'll calculate \( f(x) \) for each value of \( x \) from 0 to 5.
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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 \( x = 4 \): \[ f(4) = 320(0.75)^4 = 320(0.31640625) \approx 101 \]
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For \( x = 5 \): \[ f(5) = 320(0.75)^5 = 320(0.2373046875) \approx 76 \]
Now summarizing this in a table format:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline 0 & 320 \ 1 & 240 \ 2 & 180 \ 3 & 135 \ 4 & 101 \ 5 & 76 \ \hline \end{array} \]
These results can now be plotted on a graph to visualize the decay of the anesthetic in Cason's system over time. Each point corresponds to the values of \( x \) and \( f(x) \) calculated above.
Now, you should be able to check which graph corresponds to these plotted points. If you have the visual of the graphs, look for a graph that shows a decreasing curve that starts at 320 and eventually approaches 0, with specific points corresponding to those calculated values for each hour.
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