Use the table to answer the question. x 320 0 1 2 3 4 5 Cason is scheduled to get his wisdom teeth removed. The oral surgeon gives him a local anesthetic to numb his mouth before surgery. Cason is given 320 milligrams of the anesthetic, which metabolizes at a rate of 25% per hour. The situation can be modeled using the exponential equation f(x)=320(0.75)x . Finish the chart to determine which graph displays the correct plotted points for the situation.

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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.

  1. For \( x = 0 \): \[ f(0) = 320(0.75)^0 = 320(1) = 320 \]

  2. For \( x = 1 \): \[ f(1) = 320(0.75)^1 = 320(0.75) = 240 \]

  3. For \( x = 2 \): \[ f(2) = 320(0.75)^2 = 320(0.5625) = 180 \]

  4. For \( x = 3 \): \[ f(3) = 320(0.75)^3 = 320(0.421875) \approx 135 \]

  5. For \( x = 4 \): \[ f(4) = 320(0.75)^4 = 320(0.31640625) \approx 101 \]

  6. 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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