Use the table to answer the question.

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:

$$\text{Misplaced hline}$$

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.