Question

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. Option #1: Option #2: Option #3: (1 point) The graph with the correct plotted points is Option #

Answer 1

To complete the chart based on the exponential function \( f(x) = 320(0.75)^x \), we can calculate the values of \( f(x) \) for each \( x \) value provided in the table.

Here’s how the calculations work for each \( x \):

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

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

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

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

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

• For \( x = 5 \): \[ f(5) = 320(0.75)^5 = 320(0.2373046875) \approx 76 \]

Now, the completed table should look like this:

| x | f(x) | |---|--------| | 0 | 320 | | 1 | 240 | | 2 | 180 | | 3 | 135 | | 4 | 101 | | 5 | 76 |

With these values, you can compare the points (0, 320), (1, 240), (2, 180), (3, 135), (4, 101), and (5, 76) to each of the graph options provided (Option #1, #2, #3) to find out which graph contains all of these plotted points.

Based on this analysis, identify the graph that matches the plotted points correctly.