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 #
.
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 #
.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find which graph displays the correct plotted points for the situation where Cason is given 320 milligrams of the anesthetic that metabolizes at a rate of 25% per hour, we can calculate the values of the function \( f(x) = 320(0.75)^x \) for \( x = 0, 1, 2, 3, 4, 5 \).
Here are the calculations:
- **For \( x = 0 \)**:
\( f(0) = 320(0.75)^0 = 320 \)
- **For \( x = 1 \)**:
\( f(1) = 320(0.75)^1 = 320 \times 0.75 = 240 \)
- **For \( x = 2 \)**:
\( f(2) = 320(0.75)^2 = 320 \times 0.5625 = 180 \)
- **For \( x = 3 \)**:
\( f(3) = 320(0.75)^3 = 320 \times 0.421875 = 135 \)
- **For \( x = 4 \)**:
\( f(4) = 320(0.75)^4 = 320 \times 0.31640625 \approx 101.25 \)
- **For \( x = 5 \)**:
\( f(5) = 320(0.75)^5 = 320 \times 0.2373046875 \approx 75.0 \)
This results in the following points plotted against hours (x-values):
- \( (0, 320) \)
- \( (1, 240) \)
- \( (2, 180) \)
- \( (3, 135) \)
- \( (4, 101) \)
- \( (5, 75) \)
The values show that the function decreases over time, starting at 320 milligrams and going down with each passing hour.
Now looking at the options given:
- **Option #1** has a decreasing curve with correct axes for hours and milligrams.
- **Option #2** seems incorrectly oriented, as it has hours on the y-axis and milligrams on the x-axis.
- **Option #3** is the same as Option #1.
Thus, the correct graph with the plotted points is **Option #1** (or #3, as they are effectively the same).
So the final answer is:
The graph with the correct plotted points is Option #1.
Here are the calculations:
- **For \( x = 0 \)**:
\( f(0) = 320(0.75)^0 = 320 \)
- **For \( x = 1 \)**:
\( f(1) = 320(0.75)^1 = 320 \times 0.75 = 240 \)
- **For \( x = 2 \)**:
\( f(2) = 320(0.75)^2 = 320 \times 0.5625 = 180 \)
- **For \( x = 3 \)**:
\( f(3) = 320(0.75)^3 = 320 \times 0.421875 = 135 \)
- **For \( x = 4 \)**:
\( f(4) = 320(0.75)^4 = 320 \times 0.31640625 \approx 101.25 \)
- **For \( x = 5 \)**:
\( f(5) = 320(0.75)^5 = 320 \times 0.2373046875 \approx 75.0 \)
This results in the following points plotted against hours (x-values):
- \( (0, 320) \)
- \( (1, 240) \)
- \( (2, 180) \)
- \( (3, 135) \)
- \( (4, 101) \)
- \( (5, 75) \)
The values show that the function decreases over time, starting at 320 milligrams and going down with each passing hour.
Now looking at the options given:
- **Option #1** has a decreasing curve with correct axes for hours and milligrams.
- **Option #2** seems incorrectly oriented, as it has hours on the y-axis and milligrams on the x-axis.
- **Option #3** is the same as Option #1.
Thus, the correct graph with the plotted points is **Option #1** (or #3, as they are effectively the same).
So the final answer is:
The graph with the correct plotted points is Option #1.
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