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:

A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for hours ranges from 0 to 7 in increments of 1. The y-axis for milligrams ranges from 0 to 350 in increments of 50.



Option #2:

A curve with an arrow on the top is plotted on a coordinate plane. The x-axis for hours ranges from 0 to 350 in increments of 50. The y-axis for milligrams ranges from 0 to 7 in increments of 1.



Option #3:

A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for hours ranges from 0 to 7 in increments of 1. The y-axis for milligrams ranges from 0 to 350 in increments of 50.

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

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 \( x = 5 \).

1. **Calculate \( f(0) \)**:
\[ f(0) = 320(0.75)^0 = 320(1) = 320 \, \text{mg} \]

2. **Calculate \( f(1) \)**:
\[ f(1) = 320(0.75)^1 = 320(0.75) = 240 \, \text{mg} \]

3. **Calculate \( f(2) \)**:
\[ f(2) = 320(0.75)^2 = 320(0.5625) = 180 \, \text{mg} \]

4. **Calculate \( f(3) \)**:
\[ f(3) = 320(0.75)^3 = 320(0.421875) = 135 \, \text{mg} \]

5. **Calculate \( f(4) \)**:
\[ f(4) = 320(0.75)^4 = 320(0.31640625) \approx 101 \, \text{mg} \]

6. **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.