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.