Question

answer the question using da table

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 #
.

Answer 1

To determine the correct option, we need to calculate the amount of anesthetic remaining in Cason's system at each hour (from 0 to 5) using the given function \( f(x) = 320(0.75)^x \).

Now we will calculate \( f(x) \):

- 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 \( x = 3 \):
\[
f(3) = 320(0.75)^3 = 320(0.421875) = 135
\]

- For \( x = 4 \):
\[
f(4) = 320(0.75)^4 = 320(0.31640625) = 101.25 \approx 101
\]

- For \( x = 5 \):
\[
f(5) = 320(0.75)^5 = 320(0.2373046875) = 75.36 \approx 75
\]

Now, we can summarize the amounts remaining at each hour:

| x (hours) | f(x) (mg) |
|-----------|-----------|
| 0 | 320 |
| 1 | 240 |
| 2 | 180 |
| 3 | 135 |
| 4 | 101 |
| 5 | 75 |

Based on this data, the plotted points will show a decreasing trend as time increases, which suggests that the graph is decreasing.

Comparing this with the options:

- **Option #1:** This describes a decreasing curve, which matches our computed values.
- **Option #2:** This would not accurately reflect the situation since it suggests a curve increasing as milligrams go up with hours on the x-axis.
- **Option #3:** Also describes a decreasing curve, which matches our computed values.

Given that both Option #1 and Option #3 depict decreasing graphs, but with similar axis ranges, the correct answer would be:

The graph with the correct plotted points is Option #1.